Abstract
Identify the key drivers of brand equity for Galeries Lafayette based on a questionnaire mailed to 5000 customers and returned by 600 of themThis analysis was prepared by Francisco Arrieta and Jonathan Edwards.
# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"
# define table styling options
stable <- function(data, digits = 2) {
knitr::kable(data, digits=digits) |>
# kable_styling(c("striped", "condensed"))
kable_paper(full_width = F)
}# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs
# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr) #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test
# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion) #Histogram and Normal Curve
library(kableExtra) #makes nice tables
# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")
dim(survey)## [1] 553 45
# head(labels)#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]])
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels
#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
stable()| Variable | Category | Label_short |
|---|---|---|
| Im1 | What do GLB represent from your point of view | Large Assortment |
| Im2 | What do GLB represent from your point of view | Assortment Variety |
| Im3 | What do GLB represent from your point of view | Artistic Decoration of Sales Area |
| Im4 | What do GLB represent from your point of view | Creative Decoration of Sales Area |
| Im5 | What do GLB represent from your point of view | Appealing Arrangement of Shop Windows |
| Im6 | What do GLB represent from your point of view | France |
| Im7 | What do GLB represent from your point of view | French Savoir-vivre |
| Im8 | What do GLB represent from your point of view | Expertise in French Traditional Cuisine |
| Im9 | What do GLB represent from your point of view | French Fashion |
| Im10 | What do GLB represent from your point of view | Gourmet Food |
| Im11 | What do GLB represent from your point of view | High-quality Cosmetics |
| Im12 | What do GLB represent from your point of view | Luxury brands |
| Im13 | What do GLB represent from your point of view | Up tp date Designer Brands |
| Im14 | What do GLB represent from your point of view | Gourmet specialities |
| Im15 | What do GLB represent from your point of view | Professional Selection of Brands |
| Im16 | What do GLB represent from your point of view | Professional Appearance Towards Customers |
| Im17 | What do GLB represent from your point of view | Are Trendy |
| Im18 | What do GLB represent from your point of view | Are Hip |
| Im19 | What do GLB represent from your point of view | Professional Organization |
| Im20 | What do GLB represent from your point of view | Relaxing Shopping |
| Im21 | What do GLB represent from your point of view | A Great Place to Stroll |
| Im22 | What do GLB represent from your point of view | Intimate Shop Atmosphere |
| C_CR1 | CO-CREATION | I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin. |
| C_CR2 | CO-CREATION | I would be available to take part in another survey at Galeries Lafayette Berlin. |
| C_CR3 | CO-CREATION | I would like to become a member of a customer group whose opinion is obtained for new products and major changes. |
| C_CR4 | CO-CREATION | I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked. |
| C_REP1 | REPURCHASE | I will continue to be a loyal customer of Galeries Lafayette Berlin. |
| C_REP2 | REPURCHASE | I intend to shop at Galeries Lafayette Berlin in the future. |
| C_REP3 | REPURCAHSE | I will surely visit Galeries Lafayette Berlin in the future. |
| COM_A1 | AFFECTIVE COMMITMENT | How strongly are you attached to Galeries Lafayette Berlin? |
| COM_A2 | AFFECTIVE COMMITMENT | How strongly are you emotionally connected to Galeries Lafayette Berlin? |
| COM_A3 | AFFECTIVE COMMITMENT | As a customer I feel (close) attached to GL |
| COM_A4 | AFFECTIVE COMMITMENT | feel a strong emotional bond toward GLB |
| SAT_1 | SATISFACTION | I am very satisfied with Galeries Lafayette Berlin. |
| SAT_2 | SATISFACTION | Overall, I am very satisfied with Galeries Lafayette Berlin. |
| SAT_3 | SATISFACTION | How satisfied are you with Galeries Lafayette Berlin? |
| SAT_P1 | SATISFACTION EMPLOYEES | The employees are capable and professional. |
| SAT_P2 | SATISFACTION EMPLOYEES | The employees know best about their products. |
| SAT_P3 | SATISFACTION EMPLOYEES | The employees are well-informed. |
| SAT_P4 | SATISFACTION EMPLOYEES | The employees are always helpful. |
| SAT_P5 | SATISFACTION EMPLOYEES | The employees are willing to respond to my questions in detail. |
| SAT_P6 | SATISFACTION EMPLOYEES | The employees are friendly. |
| TRU_1 | TRUST | I have the feeling that I can completely rely on GL. |
| TRU_2 | TRUST | GLB will always be honest and trustful with me. |
| TRU_3 | TRUST | GL will treat me always fair as a customer |
# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
#
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
#
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))# delete variables unused in analysis (see case study instructions):
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))
# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c()
# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)
dim(survey)## [1] 553 35
dim(survey_excl_img)## [1] 553 35
dim(data_img_EFA)## [1] 385 22
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Variables to look out for going forward:
Images 9 and 11 are alone
Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA)
##
## X2 = 6451.238
## df = 231
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA)
##
## Measures of Sampling Adequacy (MSA):
## Im2 Im6 Im1 Im20 Im14 Im10 Im7 Im4
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604
## Im18 Im3 Im17 Im13 Im12 Im22 Im16 Im11
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882
## Im21 Im8 Im9 Im19 Im5 Im15
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563
##
## KMO-Criterion: 0.8770975
The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
# Sort table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
# Display table
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im2 | 0.82 |
| Im6 | 0.82 |
| Im1 | 0.82 |
| Im20 | 0.83 |
| Im14 | 0.83 |
| Im10 | 0.83 |
| Im7 | 0.84 |
| Im4 | 0.85 |
| Im18 | 0.86 |
| Im3 | 0.86 |
| Im17 | 0.86 |
| Im13 | 0.87 |
| Im12 | 0.88 |
| Im22 | 0.88 |
| Im16 | 0.91 |
| Im11 | 0.91 |
| Im21 | 0.91 |
| Im8 | 0.93 |
| Im9 | 0.94 |
| Im19 | 0.94 |
| Im5 | 0.95 |
| Im15 | 0.96 |
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable() | Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 8.98 | 40.81 | 0.41 |
| 2 | 2.47 | 11.21 | 0.52 |
| 3 | 1.56 | 7.10 | 0.59 |
| 4 | 1.46 | 6.62 | 0.66 |
| 5 | 1.25 | 5.67 | 0.71 |
| 6 | 1.15 | 5.22 | 0.77 |
| 7 | 0.81 | 3.68 | 0.80 |
| 8 | 0.71 | 3.23 | 0.84 |
| 9 | 0.57 | 2.58 | 0.86 |
| 10 | 0.46 | 2.08 | 0.88 |
| 11 | 0.36 | 1.64 | 0.90 |
| 12 | 0.33 | 1.51 | 0.91 |
| 13 | 0.29 | 1.34 | 0.93 |
| 14 | 0.28 | 1.29 | 0.94 |
| 15 | 0.25 | 1.13 | 0.95 |
| 16 | 0.23 | 1.04 | 0.96 |
| 17 | 0.20 | 0.92 | 0.97 |
| 18 | 0.19 | 0.85 | 0.98 |
| 19 | 0.16 | 0.72 | 0.99 |
| 20 | 0.12 | 0.53 | 0.99 |
| 21 | 0.10 | 0.46 | 1.00 |
| 22 | 0.08 | 0.37 | 1.00 |
With 6 factors we would explain 76.6310791% of total variance.
With 7 factors we would explain 80.3133487% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 8.377985
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.405600881872799”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.463399199002637”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455673655610471”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455554069181416”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR4 | MR1 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.31 | 0.18 | ||||
| Im2 | 0.83 | 1.23 | 0.24 | ||||
| Im3 | 0.83 | 1.55 | 0.14 | ||||
| Im4 | 0.87 | 1.46 | 0.08 | ||||
| Im5 | 0.64 | 1.78 | 0.45 | ||||
| Im6 | 0.67 | 1.22 | 0.50 | ||||
| Im7 | 0.79 | 1.20 | 0.31 | ||||
| Im8 | 0.84 | 1.16 | 0.24 | ||||
| Im9 | 0.43 | 0.39 | 2.76 | 0.59 | |||
| Im10 | 0.75 | 1.37 | 0.34 | ||||
| Im11 | 0.57 | 1.56 | 0.59 | ||||
| Im12 | 0.79 | 1.27 | 0.29 | ||||
| Im13 | 0.77 | 1.43 | 0.28 | ||||
| Im14 | 0.75 | 1.37 | 0.34 | ||||
| Im15 | 0.60 | 0.33 | 2.66 | 0.37 | |||
| Im16 | 0.48 | 0.37 | 2.77 | 0.54 | |||
| Im17 | 0.38 | 0.48 | 3.44 | 0.46 | |||
| Im18 | 0.31 | 0.43 | 3.42 | 0.57 | |||
| Im19 | 0.47 | 0.40 | 3.37 | 0.47 | |||
| Im20 | 0.78 | 1.27 | 0.31 | ||||
| Im21 | 0.74 | 1.41 | 0.35 | ||||
| Im22 | 0.81 | 1.51 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.30 | 0.16 | |||||
| Im2 | 0.83 | 1.24 | 0.24 | |||||
| Im3 | 0.83 | 1.51 | 0.15 | |||||
| Im4 | 0.88 | 1.42 | 0.08 | |||||
| Im5 | 0.64 | 1.74 | 0.45 | |||||
| Im6 | 0.61 | 0.56 | 2.12 | 0.29 | ||||
| Im7 | 0.72 | 0.48 | 1.88 | 0.22 | ||||
| Im8 | 0.81 | 1.25 | 0.26 | |||||
| Im9 | 0.35 | 0.32 | 0.43 | 3.51 | 0.54 | |||
| Im10 | 0.80 | 1.42 | 0.22 | |||||
| Im11 | 0.59 | 1.62 | 0.55 | |||||
| Im12 | 0.79 | 1.34 | 0.27 | |||||
| Im13 | 0.73 | 1.66 | 0.30 | |||||
| Im14 | 0.80 | 1.42 | 0.24 | |||||
| Im15 | 0.60 | 2.76 | 0.37 | |||||
| Im16 | 0.48 | 0.37 | 2.78 | 0.53 | ||||
| Im17 | 0.35 | 0.31 | 0.39 | 0.54 | 3.66 | 0.30 | ||
| Im18 | 0.35 | 0.50 | 3.48 | 0.43 | ||||
| Im19 | 0.46 | 0.40 | 3.45 | 0.48 | ||||
| Im20 | 0.84 | 1.22 | 0.21 | |||||
| Im21 | 0.73 | 1.43 | 0.35 | |||||
| Im22 | 0.79 | 1.60 | 0.21 |
| Variable | MR5 | MR1 | MR3 | MR2 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.33 | 0.14 | ||||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||||
| Im3 | 0.83 | 1.56 | 0.14 | ||||||
| Im4 | 0.90 | 1.40 | 0.03 | ||||||
| Im5 | 0.63 | 1.85 | 0.46 | ||||||
| Im6 | 0.83 | 1.25 | 0.24 | ||||||
| Im7 | 0.32 | 0.84 | 1.44 | 0.15 | |||||
| Im8 | 0.63 | 0.51 | 2.31 | 0.28 | |||||
| Im9 | 0.33 | 0.45 | 3.45 | 0.54 | |||||
| Im10 | 0.87 | 1.35 | 0.11 | ||||||
| Im11 | 0.58 | 1.72 | 0.56 | ||||||
| Im12 | 0.85 | 1.30 | 0.17 | ||||||
| Im13 | 0.72 | 1.81 | 0.30 | ||||||
| Im14 | 0.81 | 1.50 | 0.19 | ||||||
| Im15 | 0.59 | 2.97 | 0.37 | ||||||
| Im16 | 0.46 | 0.34 | 3.44 | 0.53 | |||||
| Im17 | 0.84 | 1.76 | 0.05 | ||||||
| Im18 | 0.72 | 1.85 | 0.29 | ||||||
| Im19 | 0.43 | 0.37 | 4.25 | 0.47 | |||||
| Im20 | 0.85 | 1.21 | 0.21 | ||||||
| Im21 | 0.73 | 1.44 | 0.35 | ||||||
| Im22 | 0.78 | 1.62 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR7 | MR2 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.88 | 1.45 | 0.06 | |||||||
| Im2 | 0.82 | 1.45 | 0.19 | |||||||
| Im3 | 0.81 | 1.66 | 0.14 | |||||||
| Im4 | 0.89 | 1.47 | 0.03 | |||||||
| Im5 | 0.65 | 1.84 | 0.42 | |||||||
| Im6 | 0.83 | 1.23 | 0.24 | |||||||
| Im7 | 0.84 | 0.30 | 1.40 | 0.15 | ||||||
| Im8 | 0.54 | 0.59 | 2.56 | 0.28 | ||||||
| Im9 | 0.33 | 0.46 | 3.34 | 0.54 | ||||||
| Im10 | 0.87 | 1.41 | 0.10 | |||||||
| Im11 | 0.58 | 1.72 | 0.55 | |||||||
| Im12 | 0.86 | 1.28 | 0.16 | |||||||
| Im13 | 0.72 | 1.78 | 0.30 | |||||||
| Im14 | 0.83 | 1.49 | 0.15 | |||||||
| Im15 | 0.47 | 0.39 | 4.81 | 0.35 | ||||||
| Im16 | 0.77 | 1.78 | 0.20 | |||||||
| Im17 | 0.82 | 1.82 | 0.07 | |||||||
| Im18 | 0.74 | 1.76 | 0.26 | |||||||
| Im19 | 0.30 | 0.54 | 3.68 | 0.38 | ||||||
| Im20 | 0.86 | 1.20 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.35 | |||||||
| Im22 | 0.78 | 1.63 | 0.22 |
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.
Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.
Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.
We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.272947652560888”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.339338697735652”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.279736181915467”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.302814913694533”
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.06 | 0.18 | ||||
| Im2 | 1.07 | 1.07 | 0.24 | ||||
| Im3 | 1.00 | 1.03 | 0.14 | ||||
| Im4 | 1.07 | 1.03 | 0.08 | ||||
| Im5 | 0.75 | 1.03 | 0.45 | ||||
| Im6 | 0.73 | 1.11 | 0.50 | ||||
| Im7 | 0.87 | 1.14 | 0.31 | ||||
| Im8 | 0.91 | 1.01 | 0.24 | ||||
| Im9 | 0.36 | 0.37 | 2.10 | 0.59 | |||
| Im10 | 0.77 | 1.17 | 0.34 | ||||
| Im11 | 0.69 | 1.08 | 0.59 | ||||
| Im12 | 1.00 | 1.05 | 0.29 | ||||
| Im13 | 0.94 | 1.03 | 0.28 | ||||
| Im14 | 0.77 | 1.12 | 0.34 | ||||
| Im15 | 0.62 | 1.14 | 0.37 | ||||
| Im16 | 0.47 | 1.79 | 0.54 | ||||
| Im17 | 0.42 | 2.05 | 0.46 | ||||
| Im18 | 0.39 | 1.93 | 0.57 | ||||
| Im19 | 0.41 | 2.02 | 0.47 | ||||
| Im20 | 0.86 | 1.04 | 0.31 | ||||
| Im21 | 0.79 | 1.09 | 0.35 | ||||
| Im22 | 0.85 | 1.02 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.05 | 1.06 | 0.16 | |||||
| Im2 | 1.03 | 1.07 | 0.24 | |||||
| Im3 | 0.99 | 1.03 | 0.15 | |||||
| Im4 | 1.06 | 1.05 | 0.08 | |||||
| Im5 | 0.74 | 1.03 | 0.45 | |||||
| Im6 | 0.52 | 0.68 | 2.22 | 0.29 | ||||
| Im7 | 0.65 | 0.56 | 2.24 | 0.22 | ||||
| Im8 | 0.80 | 1.05 | 0.26 | |||||
| Im9 | 0.48 | 1.95 | 0.54 | |||||
| Im10 | 0.81 | 1.23 | 0.22 | |||||
| Im11 | 0.67 | 1.15 | 0.55 | |||||
| Im12 | 0.91 | 1.03 | 0.27 | |||||
| Im13 | 0.79 | 1.09 | 0.30 | |||||
| Im14 | 0.80 | 1.18 | 0.24 | |||||
| Im15 | 0.60 | 1.18 | 0.37 | |||||
| Im16 | 0.46 | 1.81 | 0.53 | |||||
| Im17 | 0.57 | 1.97 | 0.30 | |||||
| Im18 | 0.54 | 1.91 | 0.43 | |||||
| Im19 | 0.39 | 2.15 | 0.48 | |||||
| Im20 | 0.92 | 1.07 | 0.21 | |||||
| Im21 | 0.76 | 1.07 | 0.35 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR5 | MR1 | MR2 | MR3 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.08 | 1.06 | 0.14 | ||||||
| Im2 | 1.05 | 1.06 | 0.22 | ||||||
| Im3 | 1.00 | 1.02 | 0.14 | ||||||
| Im4 | 1.13 | 1.04 | 0.03 | ||||||
| Im5 | 0.72 | 1.02 | 0.46 | ||||||
| Im6 | 0.92 | 1.06 | 0.24 | ||||||
| Im7 | 0.89 | 1.06 | 0.15 | ||||||
| Im8 | 0.62 | 0.38 | 1.74 | 0.28 | |||||
| Im9 | 0.42 | 2.10 | 0.54 | ||||||
| Im10 | 1.04 | 1.03 | 0.11 | ||||||
| Im11 | 0.65 | 1.14 | 0.56 | ||||||
| Im12 | 1.01 | 1.04 | 0.17 | ||||||
| Im13 | 0.78 | 1.08 | 0.30 | ||||||
| Im14 | 0.94 | 1.01 | 0.19 | ||||||
| Im15 | 0.60 | 1.17 | 0.37 | ||||||
| Im16 | 0.40 | 2.69 | 0.53 | ||||||
| Im17 | 1.09 | 1.02 | 0.05 | ||||||
| Im18 | 0.92 | 1.02 | 0.29 | ||||||
| Im19 | 0.33 | 3.23 | 0.47 | ||||||
| Im20 | 0.94 | 1.05 | 0.21 | ||||||
| Im21 | 0.78 | 1.06 | 0.35 | ||||||
| Im22 | 0.81 | 1.05 | 0.21 |
| Variable | MR1 | MR3 | MR7 | MR2 | MR4 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.01 | 0.06 | |||||||
| Im2 | 0.95 | 1.02 | 0.19 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.03 | 1.03 | 0.03 | |||||||
| Im5 | 0.72 | 1.11 | 0.42 | |||||||
| Im6 | 0.98 | 1.06 | 0.24 | |||||||
| Im7 | 0.95 | 1.05 | 0.15 | |||||||
| Im8 | 0.43 | 0.49 | 2.39 | 0.28 | ||||||
| Im9 | 0.45 | 1.92 | 0.54 | |||||||
| Im10 | 0.97 | 1.01 | 0.10 | |||||||
| Im11 | 0.66 | 1.15 | 0.55 | |||||||
| Im12 | 1.04 | 1.05 | 0.16 | |||||||
| Im13 | 0.79 | 1.06 | 0.30 | |||||||
| Im14 | 0.92 | 1.02 | 0.15 | |||||||
| Im15 | 0.35 | 0.36 | 2.73 | 0.35 | ||||||
| Im16 | 1.02 | 1.03 | 0.20 | |||||||
| Im17 | 0.98 | 1.01 | 0.07 | |||||||
| Im18 | 0.90 | 1.01 | 0.26 | |||||||
| Im19 | 0.63 | 1.11 | 0.38 | |||||||
| Im20 | 0.98 | 1.09 | 0.19 | |||||||
| Im21 | 0.79 | 1.06 | 0.35 | |||||||
| Im22 | 0.82 | 1.06 | 0.22 |
7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18
# # perform multiple variable selections
#
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
# c("Im3","Im4","Im9", "Im15","Im11"))
#
# survey_excl_img2 = list()
# data_img_EFA2 = list()
#
# for (i in 1:length(exclude)){
# survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
# data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
# # print(survey_excl_img2[[i]])
# }
#
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"
exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"
# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]The excluded variables correspond to the following:
excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")]
excludedvars |>
stable()| Variable | Label_short |
|---|---|
| Im8 | Expertise in French Traditional Cuisine |
| Im9 | French Fashion |
| Im15 | Professional Selection of Brands |
# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)
dim(survey)## [1] 553 35
dim(survey_excl_img2)## [1] 553 32
dim(data_img_EFA2)## [1] 394 19
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA2)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA2)
##
## X2 = 5521.451
## df = 171
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA2)
##
## Measures of Sampling Adequacy (MSA):
## Im6 Im10 Im7 Im14 Im2 Im1 Im20 Im18
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628
## Im4 Im17 Im12 Im3 Im13 Im22 Im11 Im16
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282
## Im21 Im19 Im5
## 0.9102753 0.9199391 0.9515411
##
## KMO-Criterion: 0.8416876
The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
#Display table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im6 | 0.75 |
| Im10 | 0.76 |
| Im7 | 0.77 |
| Im14 | 0.78 |
| Im2 | 0.80 |
| Im1 | 0.80 |
| Im20 | 0.81 |
| Im18 | 0.83 |
| Im4 | 0.84 |
| Im17 | 0.84 |
| Im12 | 0.85 |
| Im3 | 0.85 |
| Im13 | 0.86 |
| Im22 | 0.87 |
| Im11 | 0.90 |
| Im16 | 0.90 |
| Im21 | 0.91 |
| Im19 | 0.92 |
| Im5 | 0.95 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable()| Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 7.71 | 40.57 | 0.41 |
| 2 | 2.01 | 10.58 | 0.51 |
| 3 | 1.54 | 8.10 | 0.59 |
| 4 | 1.44 | 7.58 | 0.67 |
| 5 | 1.20 | 6.30 | 0.73 |
| 6 | 1.06 | 5.56 | 0.79 |
| 7 | 0.80 | 4.21 | 0.83 |
| 8 | 0.68 | 3.60 | 0.87 |
| 9 | 0.50 | 2.65 | 0.89 |
| 10 | 0.34 | 1.81 | 0.91 |
| 11 | 0.32 | 1.67 | 0.93 |
| 12 | 0.30 | 1.58 | 0.94 |
| 13 | 0.23 | 1.20 | 0.95 |
| 14 | 0.21 | 1.10 | 0.97 |
| 15 | 0.19 | 1.02 | 0.98 |
| 16 | 0.16 | 0.84 | 0.98 |
| 17 | 0.12 | 0.62 | 0.99 |
| 18 | 0.11 | 0.57 | 1.00 |
| 19 | 0.08 | 0.43 | 1.00 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
With 6 factors we would explain 78.6947762% of total variance.
With 7 factors we would explain 82.9058259% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 7.109148
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.496673139129337”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.638799740882147”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.931925021212407”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =0.990898460352201”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR4 | MR5 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.35 | 0.16 | ||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||
| Im3 | 0.84 | 1.44 | 0.14 | ||||
| Im4 | 0.89 | 1.36 | 0.08 | ||||
| Im5 | 0.65 | 1.66 | 0.45 | ||||
| Im6 | 0.67 | 1.23 | 0.50 | ||||
| Im7 | 0.78 | 1.20 | 0.33 | ||||
| Im10 | 0.74 | 1.42 | 0.34 | ||||
| Im11 | 0.58 | 1.49 | 0.59 | ||||
| Im12 | 0.82 | 1.22 | 0.25 | ||||
| Im13 | 0.77 | 1.44 | 0.28 | ||||
| Im14 | 0.77 | 1.39 | 0.30 | ||||
| Im16 | 0.40 | 0.41 | 3.03 | 0.58 | |||
| Im17 | 0.30 | 0.43 | 0.39 | 3.76 | 0.48 | ||
| Im18 | 0.39 | 0.32 | 3.81 | 0.58 | |||
| Im19 | 0.42 | 0.43 | 3.53 | 0.49 | |||
| Im20 | 0.80 | 1.23 | 0.28 | ||||
| Im21 | 0.74 | 1.39 | 0.36 | ||||
| Im22 | 0.81 | 1.49 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR4 | MR5 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.40 | 0.11 | |||||
| Im2 | 0.83 | 1.33 | 0.20 | |||||
| Im3 | 0.85 | 1.43 | 0.14 | |||||
| Im4 | 0.89 | 1.35 | 0.08 | |||||
| Im5 | 0.65 | 1.63 | 0.45 | |||||
| Im6 | 0.73 | 1.40 | 0.36 | |||||
| Im7 | 0.81 | 1.24 | 0.27 | |||||
| Im10 | 0.70 | 0.32 | 1.95 | 0.29 | ||||
| Im11 | 0.61 | 1.46 | 0.55 | |||||
| Im12 | 0.80 | 1.31 | 0.26 | |||||
| Im13 | 0.71 | 1.80 | 0.31 | |||||
| Im14 | 0.73 | 0.32 | 1.85 | 0.26 | ||||
| Im16 | 0.41 | 0.39 | 3.16 | 0.58 | ||||
| Im17 | 0.74 | 2.15 | 0.17 | |||||
| Im18 | 0.66 | 2.10 | 0.35 | |||||
| Im19 | 0.43 | 0.39 | 3.93 | 0.49 | ||||
| Im20 | 0.84 | 1.21 | 0.22 | |||||
| Im21 | 0.73 | 1.43 | 0.36 | |||||
| Im22 | 0.79 | 1.54 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.87 | 1.40 | 0.09 | ||||||
| Im2 | 0.83 | 1.35 | 0.19 | ||||||
| Im3 | 0.84 | 1.46 | 0.14 | ||||||
| Im4 | 0.92 | 1.33 | 0.03 | ||||||
| Im5 | 0.64 | 1.73 | 0.45 | ||||||
| Im6 | 0.93 | 1.17 | 0.07 | ||||||
| Im7 | 0.33 | 0.75 | 1.62 | 0.28 | |||||
| Im10 | 0.92 | 1.32 | 0.03 | ||||||
| Im11 | 0.57 | 1.70 | 0.57 | ||||||
| Im12 | 0.88 | 1.23 | 0.13 | ||||||
| Im13 | 0.72 | 1.76 | 0.31 | ||||||
| Im14 | 0.77 | 0.30 | 1.67 | 0.22 | |||||
| Im16 | 0.38 | 0.37 | 3.99 | 0.57 | |||||
| Im17 | 0.88 | 1.60 | 0.00 | ||||||
| Im18 | 0.70 | 1.84 | 0.33 | ||||||
| Im19 | 0.40 | 0.37 | 4.52 | 0.49 | |||||
| Im20 | 0.85 | 1.19 | 0.21 | ||||||
| Im21 | 0.73 | 1.43 | 0.36 | ||||||
| Im22 | 0.79 | 1.55 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR7 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.91 | 1.44 | 0.00 | |||||||
| Im2 | 0.78 | 1.56 | 0.24 | |||||||
| Im3 | 0.82 | 1.63 | 0.14 | |||||||
| Im4 | 0.89 | 1.46 | 0.03 | |||||||
| Im5 | 0.66 | 1.78 | 0.42 | |||||||
| Im6 | 0.96 | 1.15 | 0.01 | |||||||
| Im7 | 0.34 | 0.72 | 1.69 | 0.31 | ||||||
| Im10 | 0.93 | 1.32 | 0.00 | |||||||
| Im11 | 0.57 | 1.71 | 0.57 | |||||||
| Im12 | 0.89 | 1.22 | 0.13 | |||||||
| Im13 | 0.72 | 1.76 | 0.31 | |||||||
| Im14 | 0.77 | 1.68 | 0.22 | |||||||
| Im16 | 0.68 | 2.03 | 0.33 | |||||||
| Im17 | 0.88 | 1.65 | 0.00 | |||||||
| Im18 | 0.70 | 1.84 | 0.32 | |||||||
| Im19 | 0.64 | 2.71 | 0.30 | |||||||
| Im20 | 0.86 | 1.19 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.36 | |||||||
| Im22 | 0.79 | 1.56 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.547199381232095”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.833006250441541”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.971113915290573”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =1.14058133882705”
# loadings for all selected number of factors
test = list()
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR5 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.06 | 1.05 | 0.16 | ||||
| Im2 | 1.06 | 1.07 | 0.22 | ||||
| Im3 | 1.05 | 1.04 | 0.14 | ||||
| Im4 | 1.11 | 1.05 | 0.08 | ||||
| Im5 | 0.77 | 1.03 | 0.45 | ||||
| Im6 | 0.72 | 1.12 | 0.50 | ||||
| Im7 | 0.85 | 1.15 | 0.33 | ||||
| Im10 | 0.75 | 1.21 | 0.34 | ||||
| Im11 | 0.68 | 1.09 | 0.59 | ||||
| Im12 | 1.00 | 1.04 | 0.25 | ||||
| Im13 | 0.89 | 1.02 | 0.28 | ||||
| Im14 | 0.78 | 1.14 | 0.30 | ||||
| Im16 | 0.33 | 0.36 | 2.14 | 0.58 | |||
| Im17 | 0.34 | 2.56 | 0.48 | ||||
| Im18 | 0.31 | 2.71 | 0.58 | ||||
| Im19 | 0.32 | 0.36 | 2.28 | 0.49 | |||
| Im20 | 0.88 | 1.07 | 0.28 | ||||
| Im21 | 0.78 | 1.06 | 0.36 | ||||
| Im22 | 0.84 | 1.02 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR5 | MR4 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.05 | 0.11 | |||||
| Im2 | 1.00 | 1.04 | 0.20 | |||||
| Im3 | 1.02 | 1.05 | 0.14 | |||||
| Im4 | 1.08 | 1.05 | 0.08 | |||||
| Im5 | 0.76 | 1.03 | 0.45 | |||||
| Im6 | 0.84 | 1.39 | 0.36 | |||||
| Im7 | 0.91 | 1.18 | 0.27 | |||||
| Im10 | 0.68 | 1.69 | 0.29 | |||||
| Im11 | 0.67 | 1.05 | 0.55 | |||||
| Im12 | 0.91 | 1.06 | 0.26 | |||||
| Im13 | 0.77 | 1.22 | 0.31 | |||||
| Im14 | 0.71 | 1.55 | 0.26 | |||||
| Im16 | 0.33 | 0.33 | 2.12 | 0.58 | ||||
| Im17 | 0.77 | 1.14 | 0.17 | |||||
| Im18 | 0.69 | 1.14 | 0.35 | |||||
| Im19 | 0.33 | 2.58 | 0.49 | |||||
| Im20 | 0.91 | 1.08 | 0.22 | |||||
| Im21 | 0.75 | 1.06 | 0.36 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR1 | MR3 | MR5 | MR4 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.05 | 0.09 | ||||||
| Im2 | 1.02 | 1.03 | 0.19 | ||||||
| Im3 | 1.01 | 1.02 | 0.14 | ||||||
| Im4 | 1.14 | 1.05 | 0.03 | ||||||
| Im5 | 0.73 | 1.02 | 0.45 | ||||||
| Im6 | 0.98 | 1.04 | 0.07 | ||||||
| Im7 | 0.73 | 1.16 | 0.28 | ||||||
| Im10 | 1.10 | 1.03 | 0.03 | ||||||
| Im11 | 0.60 | 1.16 | 0.57 | ||||||
| Im12 | 1.00 | 1.03 | 0.13 | ||||||
| Im13 | 0.75 | 1.11 | 0.31 | ||||||
| Im14 | 0.87 | 1.04 | 0.22 | ||||||
| Im16 | 3.60 | 0.57 | |||||||
| Im17 | 1.12 | 1.02 | 0.00 | ||||||
| Im18 | 0.86 | 1.03 | 0.33 | ||||||
| Im19 | 3.47 | 0.49 | |||||||
| Im20 | 0.94 | 1.04 | 0.21 | ||||||
| Im21 | 0.77 | 1.05 | 0.36 | ||||||
| Im22 | 0.82 | 1.03 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR2 | MR5 | MR6 | MR7 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.03 | 1.01 | 0.00 | |||||||
| Im2 | 0.86 | 1.01 | 0.24 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.02 | 1.03 | 0.03 | |||||||
| Im5 | 0.73 | 1.09 | 0.42 | |||||||
| Im6 | 1.06 | 1.03 | 0.01 | |||||||
| Im7 | 0.72 | 1.14 | 0.31 | |||||||
| Im10 | 1.05 | 1.02 | 0.00 | |||||||
| Im11 | 0.60 | 1.15 | 0.57 | |||||||
| Im12 | 1.02 | 1.04 | 0.13 | |||||||
| Im13 | 0.75 | 1.09 | 0.31 | |||||||
| Im14 | 0.82 | 1.03 | 0.22 | |||||||
| Im16 | 0.80 | 1.02 | 0.33 | |||||||
| Im17 | 1.03 | 1.01 | 0.00 | |||||||
| Im18 | 0.81 | 1.00 | 0.32 | |||||||
| Im19 | 0.72 | 1.04 | 0.30 | |||||||
| Im20 | 0.97 | 1.09 | 0.19 | |||||||
| Im21 | 0.77 | 1.05 | 0.36 | |||||||
| Im22 | 0.82 | 1.04 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
We test whether the constructs found in the exploratory phase adequately describe what is going on.
# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")
summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 110 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
##
## Number of observations 553
## Number of missing patterns 87
##
## Model Test User Model:
##
## Test statistic 1442.584
## Degrees of freedom 194
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8838.959
## Degrees of freedom 231
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.855
## Tucker-Lewis Index (TLI) 0.827
##
## Robust Comparative Fit Index (CFI) 0.854
## Robust Tucker-Lewis Index (TLI) 0.827
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -15479.697
## Loglikelihood unrestricted model (H1) -14758.405
##
## Akaike (AIC) 31121.394
## Bayesian (BIC) 31470.938
## Sample-size adjusted Bayesian (SABIC) 31213.808
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.108
## 90 Percent confidence interval - lower 0.103
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Robust RMSEA 0.110
## 90 Percent confidence interval - lower 0.105
## 90 Percent confidence interval - upper 0.116
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.092
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.936
## Im4 1.057 0.025 42.551 0.000 1.307 0.970
## Im5 0.820 0.034 23.857 0.000 1.013 0.761
## FRENCH =~
## Im6 1.000 0.642 0.535
## Im7 1.219 0.106 11.525 0.000 0.783 0.644
## Im8 1.244 0.099 12.567 0.000 0.799 0.755
## Im10 1.251 0.095 13.133 0.000 0.803 0.914
## Im14 1.244 0.095 13.142 0.000 0.799 0.929
## ATMOS =~
## Im20 1.000 1.268 0.848
## Im21 0.848 0.041 20.879 0.000 1.075 0.785
## Im22 1.053 0.046 22.697 0.000 1.335 0.873
## QUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.050 0.000 0.991 0.872
## Im13 1.465 0.105 13.982 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.232 0.926
## Im2 0.942 0.027 34.780 0.000 1.160 0.902
## Im15 0.720 0.036 20.097 0.000 0.887 0.740
## Im16 0.567 0.041 13.849 0.000 0.699 0.579
## Im19 0.540 0.038 14.310 0.000 0.666 0.592
## BRAND =~
## Im17 1.000 1.184 0.952
## Im18 1.025 0.038 27.280 0.000 1.214 0.868
## Im9 0.540 0.047 11.386 0.000 0.640 0.474
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FRENCH 0.344 0.046 7.416 0.000 0.434 0.434
## ATMOS 0.730 0.082 8.901 0.000 0.466 0.466
## QUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.782 0.079 9.940 0.000 0.514 0.514
## BRAND 0.778 0.076 10.268 0.000 0.531 0.531
## FRENCH ~~
## ATMOS 0.265 0.045 5.888 0.000 0.326 0.326
## QUAL 0.206 0.030 6.812 0.000 0.456 0.456
## CHOICE 0.299 0.044 6.737 0.000 0.378 0.378
## BRAND 0.277 0.042 6.547 0.000 0.364 0.364
## ATMOS ~~
## QUAL 0.373 0.053 7.021 0.000 0.419 0.419
## CHOICE 0.767 0.083 9.216 0.000 0.491 0.491
## BRAND 0.792 0.081 9.797 0.000 0.528 0.528
## QUAL ~~
## CHOICE 0.460 0.054 8.585 0.000 0.531 0.531
## BRAND 0.483 0.053 9.113 0.000 0.581 0.581
## CHOICE ~~
## BRAND 0.864 0.078 11.040 0.000 0.592 0.592
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.994 0.056 88.528 0.000 4.994 3.785
## .Im4 4.997 0.057 86.919 0.000 4.997 3.709
## .Im5 5.034 0.057 87.796 0.000 5.034 3.785
## .Im6 5.824 0.051 113.338 0.000 5.824 4.849
## .Im7 5.751 0.053 109.497 0.000 5.751 4.727
## .Im8 6.000 0.045 133.008 0.000 6.000 5.671
## .Im10 6.100 0.037 163.041 0.000 6.100 6.945
## .Im14 6.139 0.037 166.909 0.000 6.139 7.138
## .Im20 4.672 0.064 73.182 0.000 4.672 3.124
## .Im21 5.139 0.058 87.973 0.000 5.139 3.751
## .Im22 4.278 0.065 65.391 0.000 4.278 2.798
## .Im11 5.653 0.049 115.277 0.000 5.653 4.943
## .Im12 5.666 0.049 116.095 0.000 5.666 4.983
## .Im13 5.448 0.052 105.630 0.000 5.448 4.525
## .Im1 4.792 0.057 84.316 0.000 4.792 3.601
## .Im2 4.861 0.055 88.357 0.000 4.861 3.779
## .Im15 5.090 0.051 99.219 0.000 5.090 4.246
## .Im16 5.130 0.052 98.387 0.000 5.130 4.251
## .Im19 5.146 0.048 106.829 0.000 5.146 4.578
## .Im17 5.025 0.053 94.490 0.000 5.025 4.038
## .Im18 4.595 0.060 76.460 0.000 4.595 3.286
## .Im9 5.075 0.058 87.318 0.000 5.075 3.757
## DECO 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## QUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.215 0.024 8.776 0.000 0.215 0.123
## .Im4 0.108 0.024 4.439 0.000 0.108 0.060
## .Im5 0.744 0.049 15.192 0.000 0.744 0.421
## .Im6 1.030 0.066 15.665 0.000 1.030 0.714
## .Im7 0.867 0.059 14.739 0.000 0.867 0.586
## .Im8 0.482 0.034 14.159 0.000 0.482 0.430
## .Im10 0.127 0.013 9.840 0.000 0.127 0.164
## .Im14 0.101 0.012 8.329 0.000 0.101 0.137
## .Im20 0.629 0.061 10.379 0.000 0.629 0.281
## .Im21 0.721 0.057 12.668 0.000 0.721 0.384
## .Im22 0.554 0.063 8.781 0.000 0.554 0.237
## .Im11 0.814 0.055 14.805 0.000 0.814 0.622
## .Im12 0.310 0.039 7.857 0.000 0.310 0.240
## .Im13 0.390 0.044 8.777 0.000 0.390 0.269
## .Im1 0.253 0.035 7.312 0.000 0.253 0.143
## .Im2 0.308 0.033 9.422 0.000 0.308 0.186
## .Im15 0.651 0.048 13.673 0.000 0.651 0.453
## .Im16 0.968 0.065 14.927 0.000 0.968 0.664
## .Im19 0.820 0.055 14.954 0.000 0.820 0.649
## .Im17 0.146 0.036 4.039 0.000 0.146 0.094
## .Im18 0.482 0.046 10.494 0.000 0.482 0.247
## .Im9 1.415 0.089 15.908 0.000 1.415 0.776
## DECO 1.527 0.107 14.308 0.000 1.000 1.000
## FRENCH 0.412 0.064 6.422 0.000 1.000 1.000
## ATMOS 1.608 0.138 11.683 0.000 1.000 1.000
## QUAL 0.494 0.067 7.365 0.000 1.000 1.000
## CHOICE 1.518 0.110 13.746 0.000 1.000 1.000
## BRAND 1.402 0.100 14.036 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## Im3 NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN
## Im6 NaN 0.286 NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN 0.336 NaN
## Im19 NaN NaN NaN NaN 0.351 NaN
## Im17 NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN 0.224
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1
## FRENCH NaN 1
## ATMOS NaN NaN 1
## QUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
psi## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1.000
## FRENCH 0.434 1.000
## ATMOS 0.466 0.326 1.000
## QUAL 0.471 0.456 0.419 1.000
## CHOICE 0.514 0.378 0.491 0.531 1.000
## BRAND 0.531 0.364 0.528 0.581 0.592 1.000
AVEpsi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO .
## FRENCH NaN .
## ATMOS NaN NaN .
## QUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN -0.011 .
arrange(modificationindices(CFA_fit_img_6f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im1 ~~ Im2 495.934 0.951 0.951 3.408 3.408
## 2 Im10 ~~ Im14 298.631 0.357 0.357 3.154 3.154
## 3 Im6 ~~ Im7 255.917 0.693 0.693 0.734 0.734
## 4 Im16 ~~ Im19 128.231 0.463 0.463 0.519 0.519
## 5 Im7 ~~ Im8 104.366 0.316 0.316 0.489 0.489
## 6 DECO =~ Im19 76.462 0.344 0.424 0.378 0.378
## 7 FRENCH =~ Im9 73.482 0.783 0.503 0.372 0.372
## 8 Im6 ~~ Im10 55.895 -0.158 -0.158 -0.438 -0.438
## 9 Im1 ~~ Im16 55.410 -0.242 -0.242 -0.489 -0.489
## 10 QUAL =~ Im15 54.596 0.510 0.359 0.299 0.299
## 11 Im6 ~~ Im8 52.130 0.236 0.236 0.335 0.335
## 12 Im7 ~~ Im14 50.063 -0.145 -0.145 -0.491 -0.491
## 13 FRENCH =~ Im19 49.872 0.497 0.319 0.284 0.284
## 14 Im15 ~~ Im16 49.062 0.263 0.263 0.332 0.332
## 15 Im1 ~~ Im19 46.763 -0.204 -0.204 -0.449 -0.449
## 16 QUAL =~ Im9 45.834 0.702 0.494 0.365 0.365
## 17 Im2 ~~ Im19 45.384 -0.198 -0.198 -0.393 -0.393
## 18 Im7 ~~ Im9 45.214 0.340 0.340 0.307 0.307
## 19 DECO =~ Im16 44.633 0.288 0.356 0.295 0.295
## 20 BRAND =~ Im19 43.739 0.300 0.355 0.316 0.316
## 21 Im7 ~~ Im10 41.088 -0.134 -0.134 -0.406 -0.406
## 22 QUAL =~ Im2 38.006 -0.361 -0.254 -0.197 -0.197
## 23 BRAND =~ Im15 37.135 0.254 0.301 0.251 0.251
## 24 Im17 ~~ Im18 36.588 0.762 0.762 2.870 2.870
## 25 Im2 ~~ Im15 35.103 -0.179 -0.179 -0.399 -0.399
## 26 Im15 ~~ Im19 34.736 0.202 0.202 0.277 0.277
## 27 QUAL =~ Im19 33.294 0.434 0.305 0.271 0.271
## 28 Im8 ~~ Im14 32.038 -0.103 -0.103 -0.467 -0.467
## 29 Im6 ~~ Im9 31.342 0.301 0.301 0.249 0.249
## 30 Im1 ~~ Im15 30.586 -0.174 -0.174 -0.429 -0.429
## 31 Im2 ~~ Im16 28.333 -0.170 -0.170 -0.311 -0.311
## 32 DECO =~ Im15 27.803 0.191 0.236 0.197 0.197
## 33 Im6 ~~ Im14 27.360 -0.108 -0.108 -0.335 -0.335
## 34 FRENCH =~ Im16 27.263 0.403 0.259 0.214 0.214
## 35 DECO =~ Im2 26.666 -0.158 -0.195 -0.152 -0.152
## 36 ATMOS =~ Im15 24.669 0.181 0.230 0.192 0.192
## 37 BRAND =~ Im13 23.589 0.232 0.275 0.228 0.228
## 38 DECO =~ Im1 22.892 -0.149 -0.184 -0.138 -0.138
## 39 ATMOS =~ Im2 21.308 -0.142 -0.180 -0.140 -0.140
## 40 Im11 ~~ Im13 21.300 -0.191 -0.191 -0.339 -0.339
## 41 BRAND =~ Im2 21.047 -0.165 -0.195 -0.152 -0.152
## 42 FRENCH =~ Im1 20.125 -0.244 -0.156 -0.118 -0.118
## 43 FRENCH =~ Im15 18.582 0.279 0.179 0.149 0.149
## 44 BRAND =~ Im12 18.526 -0.197 -0.233 -0.205 -0.205
## 45 BRAND =~ Im16 17.630 0.209 0.247 0.205 0.205
## 46 BRAND =~ Im1 16.671 -0.150 -0.177 -0.133 -0.133
## 47 ATMOS =~ Im19 16.384 0.161 0.204 0.181 0.181
## 48 BRAND =~ Im6 14.589 0.161 0.191 0.159 0.159
## 49 CHOICE =~ Im20 14.430 -0.169 -0.208 -0.139 -0.139
## 50 Im14 ~~ Im9 13.864 -0.082 -0.082 -0.217 -0.217
## 51 Im11 ~~ Im12 13.374 0.145 0.145 0.289 0.289
## 52 Im21 ~~ Im22 13.217 -0.270 -0.270 -0.427 -0.427
## 53 CHOICE =~ Im13 13.044 0.152 0.187 0.155 0.155
## 54 ATMOS =~ Im7 12.806 0.134 0.170 0.140 0.140
## 55 Im8 ~~ Im10 12.666 -0.065 -0.065 -0.265 -0.265
## 56 FRENCH =~ Im11 12.345 0.269 0.173 0.151 0.151
## 57 CHOICE =~ Im12 11.541 -0.136 -0.168 -0.148 -0.148
## 58 Im3 ~~ Im4 11.447 0.264 0.264 1.735 1.735
## 59 ATMOS =~ Im16 11.243 0.146 0.185 0.153 0.153
## 60 ATMOS =~ Im12 11.072 -0.115 -0.146 -0.128 -0.128
## 61 Im8 ~~ Im9 10.943 0.125 0.125 0.152 0.152
## 62 FRENCH =~ Im2 10.891 -0.177 -0.114 -0.088 -0.088
## 63 Im7 ~~ Im22 10.253 0.126 0.126 0.182 0.182
## 64 DECO =~ Im9 10.194 0.167 0.207 0.153 0.153
## 65 Im11 ~~ Im9 10.067 0.156 0.156 0.145 0.145
## 66 Im15 ~~ Im9 9.926 0.139 0.139 0.145 0.145
## 67 QUAL =~ Im16 9.231 0.250 0.176 0.146 0.146
## 68 Im8 ~~ Im15 9.159 0.080 0.080 0.144 0.144
## 69 ATMOS =~ Im9 9.070 0.162 0.205 0.152 0.152
## 70 Im13 ~~ Im17 9.051 0.067 0.067 0.281 0.281
## 71 Im6 ~~ Im22 8.985 0.125 0.125 0.166 0.166
## 72 Im20 ~~ Im21 8.930 0.206 0.206 0.306 0.306
## 73 BRAND =~ Im22 8.880 0.147 0.175 0.114 0.114
## 74 Im8 ~~ Im16 8.801 0.095 0.095 0.139 0.139
## 75 BRAND =~ Im20 8.486 -0.141 -0.167 -0.111 -0.111
## 76 BRAND =~ Im7 8.244 0.114 0.135 0.111 0.111
## 77 Im3 ~~ Im1 8.143 -0.045 -0.045 -0.194 -0.194
## 78 Im8 ~~ Im2 7.823 -0.059 -0.059 -0.153 -0.153
## 79 QUAL =~ Im18 7.388 -0.230 -0.161 -0.115 -0.115
## 80 Im10 ~~ Im16 7.338 0.052 0.052 0.149 0.149
## 81 Im13 ~~ Im1 7.263 0.060 0.060 0.191 0.191
## 82 Im4 ~~ Im17 7.109 -0.041 -0.041 -0.322 -0.322
## 83 Im22 ~~ Im12 7.028 -0.078 -0.078 -0.189 -0.189
## 84 Im17 ~~ Im9 7.005 -0.112 -0.112 -0.247 -0.247
## 85 DECO =~ Im6 6.969 0.109 0.134 0.112 0.112
## 86 ATMOS =~ Im11 6.857 0.102 0.130 0.113 0.113
## 87 CHOICE =~ Im9 6.692 0.148 0.182 0.135 0.135
## 88 ATMOS =~ Im6 6.616 0.102 0.130 0.108 0.108
## 89 Im14 ~~ Im2 6.285 0.031 0.031 0.175 0.175
## 90 BRAND =~ Im5 6.246 0.103 0.122 0.092 0.092
## 91 BRAND =~ Im4 6.180 -0.071 -0.084 -0.062 -0.062
## 92 Im22 ~~ Im9 5.999 0.121 0.121 0.136 0.136
## 93 QUAL =~ Im5 5.978 0.169 0.119 0.089 0.089
## 94 Im1 ~~ Im9 5.822 -0.084 -0.084 -0.140 -0.140
## 95 QUAL =~ Im1 5.747 -0.143 -0.100 -0.075 -0.075
## 96 CHOICE =~ Im18 5.737 -0.115 -0.141 -0.101 -0.101
## 97 Im3 ~~ Im5 5.693 -0.084 -0.084 -0.209 -0.209
## 98 Im8 ~~ Im22 5.661 0.070 0.070 0.136 0.136
## 99 DECO =~ Im20 5.578 -0.100 -0.123 -0.082 -0.082
## 100 ATMOS =~ Im5 5.473 0.089 0.112 0.084 0.084
## 101 DECO =~ Im17 5.404 -0.091 -0.112 -0.090 -0.090
## 102 Im11 ~~ Im17 5.351 -0.061 -0.061 -0.177 -0.177
## 103 CHOICE =~ Im5 5.052 0.088 0.108 0.082 0.082
## 104 FRENCH =~ Im13 4.802 -0.157 -0.101 -0.084 -0.084
## 105 DECO =~ Im22 4.756 0.094 0.116 0.076 0.076
## 106 Im22 ~~ Im11 4.722 0.083 0.083 0.124 0.124
## 107 CHOICE =~ Im22 4.719 0.099 0.122 0.080 0.080
## 108 Im13 ~~ Im16 4.625 -0.073 -0.073 -0.118 -0.118
## 109 Im19 ~~ Im17 4.621 0.056 0.056 0.161 0.161
## 110 ATMOS =~ Im10 4.609 -0.038 -0.048 -0.055 -0.055
## 111 BRAND =~ Im10 4.570 -0.040 -0.048 -0.054 -0.054
## 112 Im14 ~~ Im22 4.494 -0.036 -0.036 -0.154 -0.154
## 113 ATMOS =~ Im4 4.422 -0.053 -0.067 -0.050 -0.050
## 114 Im14 ~~ Im15 4.415 -0.032 -0.032 -0.127 -0.127
## 115 Im21 ~~ Im9 4.370 -0.102 -0.102 -0.101 -0.101
## 116 Im10 ~~ Im13 4.362 -0.031 -0.031 -0.138 -0.138
## 117 Im7 ~~ Im15 4.358 0.074 0.074 0.098 0.098
## 118 Im3 ~~ Im22 4.300 0.047 0.047 0.135 0.135
## 119 Im20 ~~ Im1 4.283 -0.056 -0.056 -0.141 -0.141
## 120 Im4 ~~ Im16 4.262 0.048 0.048 0.149 0.149
## 121 FRENCH =~ Im5 4.167 0.144 0.093 0.070 0.070
## 122 ATMOS =~ Im8 4.061 0.057 0.072 0.068 0.068
## 123 Im6 ~~ Im20 4.039 -0.084 -0.084 -0.105 -0.105
## 124 Im10 ~~ Im11 4.002 0.036 0.036 0.111 0.111
## 125 Im20 ~~ Im17 3.990 -0.054 -0.054 -0.177 -0.177
## 126 Im6 ~~ Im11 3.977 -0.083 -0.083 -0.091 -0.091
## 127 Im5 ~~ Im1 3.869 0.051 0.051 0.117 0.117
## 128 Im15 ~~ Im17 3.695 0.045 0.045 0.147 0.147
## 129 Im4 ~~ Im18 3.604 0.035 0.035 0.152 0.152
## 130 Im12 ~~ Im15 3.556 0.050 0.050 0.110 0.110
## 131 FRENCH =~ Im17 3.536 -0.115 -0.074 -0.060 -0.060
## 132 Im14 ~~ Im16 3.474 -0.035 -0.035 -0.110 -0.110
## 133 Im3 ~~ Im15 3.381 0.037 0.037 0.099 0.099
## 134 Im3 ~~ Im17 3.375 0.029 0.029 0.161 0.161
## 135 Im3 ~~ Im19 3.371 0.040 0.040 0.096 0.096
## 136 Im13 ~~ Im15 3.338 0.051 0.051 0.102 0.102
## 137 Im22 ~~ Im1 3.275 0.049 0.049 0.132 0.132
## 138 Im20 ~~ Im13 3.270 0.057 0.057 0.115 0.115
## 139 Im13 ~~ Im2 3.219 -0.040 -0.040 -0.116 -0.116
## 140 Im11 ~~ Im1 3.071 -0.047 -0.047 -0.104 -0.104
## 141 CHOICE =~ Im21 3.048 0.074 0.091 0.066 0.066
## 142 Im10 ~~ Im17 3.000 -0.021 -0.021 -0.157 -0.157
## 143 ATMOS =~ Im1 2.962 -0.054 -0.068 -0.051 -0.051
## 144 ATMOS =~ Im13 2.889 0.062 0.078 0.065 0.065
## 145 Im16 ~~ Im9 2.810 0.089 0.089 0.076 0.076
## 146 Im5 ~~ Im14 2.794 0.028 0.028 0.101 0.101
## 147 Im4 ~~ Im22 2.701 -0.036 -0.036 -0.146 -0.146
## 148 CHOICE =~ Im10 2.670 -0.030 -0.037 -0.042 -0.042
## 149 Im1 ~~ Im17 2.662 -0.031 -0.031 -0.161 -0.161
## 150 ATMOS =~ Im14 2.649 -0.028 -0.035 -0.041 -0.041
## 151 Im4 ~~ Im19 2.526 0.034 0.034 0.113 0.113
## 152 Im4 ~~ Im11 2.492 -0.034 -0.034 -0.115 -0.115
## 153 Im21 ~~ Im18 2.456 -0.050 -0.050 -0.086 -0.086
## 154 Im12 ~~ Im2 2.343 -0.032 -0.032 -0.104 -0.104
## 155 Im6 ~~ Im15 2.316 0.057 0.057 0.070 0.070
## 156 Im12 ~~ Im9 2.302 0.057 0.057 0.086 0.086
## 157 DECO =~ Im12 2.287 -0.054 -0.067 -0.059 -0.059
## 158 Im6 ~~ Im1 2.248 -0.044 -0.044 -0.087 -0.087
## 159 Im3 ~~ Im20 2.237 -0.034 -0.034 -0.091 -0.091
## 160 Im15 ~~ Im18 2.236 -0.043 -0.043 -0.077 -0.077
## 161 Im7 ~~ Im1 2.236 -0.042 -0.042 -0.089 -0.089
## 162 Im6 ~~ Im12 2.164 -0.047 -0.047 -0.083 -0.083
## 163 Im10 ~~ Im12 2.160 0.020 0.020 0.102 0.102
## 164 Im4 ~~ Im2 2.090 -0.022 -0.022 -0.123 -0.123
## 165 Im5 ~~ Im6 1.873 -0.055 -0.055 -0.063 -0.063
## 166 Im4 ~~ Im6 1.846 0.032 0.032 0.096 0.096
## 167 DECO =~ Im10 1.832 -0.025 -0.031 -0.035 -0.035
## 168 Im22 ~~ Im2 1.825 -0.037 -0.037 -0.090 -0.090
## 169 Im10 ~~ Im22 1.781 -0.024 -0.024 -0.090 -0.090
## 170 Im12 ~~ Im17 1.776 -0.028 -0.028 -0.131 -0.131
## 171 Im6 ~~ Im18 1.754 0.047 0.047 0.066 0.066
## 172 Im21 ~~ Im17 1.749 0.035 0.035 0.108 0.108
## 173 Im5 ~~ Im16 1.746 -0.052 -0.052 -0.062 -0.062
## 174 Im3 ~~ Im12 1.732 -0.023 -0.023 -0.087 -0.087
## 175 Im22 ~~ Im13 1.726 -0.041 -0.041 -0.089 -0.089
## 176 Im18 ~~ Im9 1.696 -0.060 -0.060 -0.073 -0.073
## 177 ATMOS =~ Im17 1.682 -0.052 -0.065 -0.053 -0.053
## 178 QUAL =~ Im4 1.672 -0.060 -0.042 -0.031 -0.031
## 179 Im20 ~~ Im19 1.649 0.048 0.048 0.067 0.067
## 180 Im20 ~~ Im2 1.631 -0.035 -0.035 -0.080 -0.080
## 181 FRENCH =~ Im18 1.599 -0.082 -0.052 -0.038 -0.038
## 182 Im4 ~~ Im12 1.546 0.021 0.021 0.113 0.113
## 183 CHOICE =~ Im17 1.544 0.057 0.071 0.057 0.057
## 184 Im6 ~~ Im19 1.483 0.050 0.050 0.055 0.055
## 185 Im12 ~~ Im16 1.481 0.038 0.038 0.070 0.070
## 186 Im7 ~~ Im16 1.479 -0.052 -0.052 -0.056 -0.056
## 187 DECO =~ Im13 1.462 0.045 0.056 0.046 0.046
## 188 FRENCH =~ Im20 1.442 -0.089 -0.057 -0.038 -0.038
## 189 Im12 ~~ Im13 1.442 0.089 0.089 0.255 0.255
## 190 BRAND =~ Im3 1.434 0.033 0.039 0.030 0.030
## 191 Im12 ~~ Im1 1.360 -0.024 -0.024 -0.087 -0.087
## 192 Im3 ~~ Im18 1.301 -0.022 -0.022 -0.067 -0.067
## 193 Im16 ~~ Im17 1.269 0.032 0.032 0.085 0.085
## 194 Im3 ~~ Im11 1.261 0.025 0.025 0.060 0.060
## 195 Im14 ~~ Im17 1.252 0.013 0.013 0.110 0.110
## 196 Im10 ~~ Im19 1.233 0.019 0.019 0.060 0.060
## 197 Im3 ~~ Im10 1.230 0.012 0.012 0.070 0.070
## 198 Im8 ~~ Im18 1.200 -0.027 -0.027 -0.057 -0.057
## 199 Im8 ~~ Im1 1.194 -0.023 -0.023 -0.065 -0.065
## 200 Im21 ~~ Im2 1.185 0.030 0.030 0.063 0.063
## 201 QUAL =~ Im22 1.168 -0.084 -0.059 -0.038 -0.038
## 202 CHOICE =~ Im14 1.154 0.019 0.023 0.027 0.027
## 203 Im10 ~~ Im9 1.119 0.024 0.024 0.057 0.057
## 204 DECO =~ Im18 1.115 0.043 0.053 0.038 0.038
## 205 CHOICE =~ Im4 1.111 -0.028 -0.035 -0.026 -0.026
## 206 Im14 ~~ Im21 1.104 0.018 0.018 0.067 0.067
## 207 Im5 ~~ Im19 1.093 -0.038 -0.038 -0.048 -0.048
## 208 Im4 ~~ Im8 1.089 0.017 0.017 0.076 0.076
## 209 Im22 ~~ Im18 1.078 0.034 0.034 0.065 0.065
## 210 Im22 ~~ Im15 1.067 0.036 0.036 0.059 0.059
## 211 Im13 ~~ Im18 1.031 -0.027 -0.027 -0.062 -0.062
## 212 CHOICE =~ Im7 0.941 0.037 0.046 0.038 0.038
## 213 Im4 ~~ Im10 0.906 -0.010 -0.010 -0.082 -0.082
## 214 Im3 ~~ Im14 0.890 -0.010 -0.010 -0.065 -0.065
## 215 Im10 ~~ Im2 0.889 -0.012 -0.012 -0.061 -0.061
## 216 ATMOS =~ Im3 0.869 0.023 0.029 0.022 0.022
## 217 Im11 ~~ Im16 0.846 0.038 0.038 0.043 0.043
## 218 QUAL =~ Im14 0.840 0.031 0.022 0.026 0.026
## 219 QUAL =~ Im20 0.837 0.069 0.049 0.033 0.033
## 220 Im1 ~~ Im18 0.830 0.021 0.021 0.060 0.060
## 221 Im3 ~~ Im16 0.818 0.022 0.022 0.048 0.048
## 222 DECO =~ Im7 0.814 0.035 0.043 0.036 0.036
## 223 Im2 ~~ Im18 0.811 -0.021 -0.021 -0.054 -0.054
## 224 Im20 ~~ Im12 0.794 0.026 0.026 0.059 0.059
## 225 FRENCH =~ Im22 0.781 0.067 0.043 0.028 0.028
## 226 Im20 ~~ Im16 0.767 0.036 0.036 0.046 0.046
## 227 Im14 ~~ Im18 0.739 -0.012 -0.012 -0.056 -0.056
## 228 Im22 ~~ Im19 0.717 -0.032 -0.032 -0.047 -0.047
## 229 QUAL =~ Im10 0.654 -0.028 -0.020 -0.023 -0.023
## 230 Im14 ~~ Im13 0.649 0.011 0.011 0.057 0.057
## 231 Im14 ~~ Im11 0.639 0.014 0.014 0.048 0.048
## 232 CHOICE =~ Im6 0.612 0.032 0.039 0.033 0.033
## 233 Im19 ~~ Im9 0.595 0.037 0.037 0.035 0.035
## 234 BRAND =~ Im11 0.591 -0.036 -0.043 -0.038 -0.038
## 235 Im6 ~~ Im2 0.577 -0.023 -0.023 -0.040 -0.040
## 236 Im20 ~~ Im15 0.576 0.026 0.026 0.041 0.041
## 237 Im5 ~~ Im22 0.561 0.027 0.027 0.043 0.043
## 238 Im8 ~~ Im19 0.558 0.022 0.022 0.035 0.035
## 239 Im8 ~~ Im21 0.538 -0.022 -0.022 -0.037 -0.037
## 240 Im21 ~~ Im12 0.537 0.021 0.021 0.045 0.045
## 241 Im11 ~~ Im19 0.536 0.028 0.028 0.034 0.034
## 242 Im21 ~~ Im1 0.534 0.020 0.020 0.046 0.046
## 243 QUAL =~ Im7 0.517 0.053 0.037 0.031 0.031
## 244 Im10 ~~ Im18 0.516 0.011 0.011 0.044 0.044
## 245 Im5 ~~ Im11 0.511 0.026 0.026 0.034 0.034
## 246 Im10 ~~ Im20 0.483 0.012 0.012 0.044 0.044
## 247 Im12 ~~ Im18 0.465 -0.017 -0.017 -0.044 -0.044
## 248 Im14 ~~ Im1 0.460 0.008 0.008 0.052 0.052
## 249 FRENCH =~ Im3 0.457 -0.031 -0.020 -0.015 -0.015
## 250 Im20 ~~ Im11 0.453 0.026 0.026 0.036 0.036
## 251 Im3 ~~ Im8 0.442 -0.012 -0.012 -0.036 -0.036
## 252 Im20 ~~ Im18 0.417 0.021 0.021 0.038 0.038
## 253 Im20 ~~ Im22 0.407 0.061 0.061 0.103 0.103
## 254 Im10 ~~ Im1 0.405 -0.008 -0.008 -0.045 -0.045
## 255 Im5 ~~ Im20 0.402 0.023 0.023 0.034 0.034
## 256 BRAND =~ Im14 0.390 -0.011 -0.014 -0.016 -0.016
## 257 Im2 ~~ Im9 0.381 -0.022 -0.022 -0.033 -0.033
## 258 Im21 ~~ Im11 0.373 -0.023 -0.023 -0.030 -0.030
## 259 Im16 ~~ Im18 0.357 -0.021 -0.021 -0.030 -0.030
## 260 Im5 ~~ Im15 0.339 -0.019 -0.019 -0.028 -0.028
## 261 Im21 ~~ Im13 0.328 -0.018 -0.018 -0.034 -0.034
## 262 QUAL =~ Im8 0.320 -0.031 -0.022 -0.021 -0.021
## 263 Im5 ~~ Im21 0.319 -0.021 -0.021 -0.028 -0.028
## 264 DECO =~ Im8 0.317 0.016 0.020 0.019 0.019
## 265 Im7 ~~ Im19 0.317 0.022 0.022 0.026 0.026
## 266 Im4 ~~ Im20 0.315 0.012 0.012 0.047 0.047
## 267 Im11 ~~ Im2 0.310 0.015 0.015 0.030 0.030
## 268 Im5 ~~ Im8 0.298 -0.015 -0.015 -0.026 -0.026
## 269 Im7 ~~ Im20 0.292 -0.021 -0.021 -0.029 -0.029
## 270 Im4 ~~ Im13 0.275 -0.009 -0.009 -0.045 -0.045
## 271 Im3 ~~ Im13 0.274 0.010 0.010 0.033 0.033
## 272 Im8 ~~ Im13 0.252 -0.012 -0.012 -0.028 -0.028
## 273 DECO =~ Im11 0.240 0.019 0.024 0.021 0.021
## 274 Im12 ~~ Im19 0.218 0.013 0.013 0.027 0.027
## 275 Im4 ~~ Im5 0.193 0.017 0.017 0.059 0.059
## 276 Im3 ~~ Im7 0.193 -0.010 -0.010 -0.024 -0.024
## 277 Im7 ~~ Im12 0.191 -0.013 -0.013 -0.025 -0.025
## 278 Im5 ~~ Im17 0.190 0.011 0.011 0.033 0.033
## 279 Im7 ~~ Im21 0.188 -0.017 -0.017 -0.022 -0.022
## 280 Im5 ~~ Im9 0.179 0.020 0.020 0.019 0.019
## 281 Im19 ~~ Im18 0.174 -0.013 -0.013 -0.021 -0.021
## 282 Im21 ~~ Im16 0.170 -0.017 -0.017 -0.020 -0.020
## 283 FRENCH =~ Im4 0.152 -0.018 -0.012 -0.009 -0.009
## 284 Im4 ~~ Im15 0.151 -0.008 -0.008 -0.028 -0.028
## 285 Im21 ~~ Im19 0.149 -0.014 -0.014 -0.019 -0.019
## 286 DECO =~ Im14 0.132 -0.007 -0.008 -0.009 -0.009
## 287 Im4 ~~ Im1 0.125 0.005 0.005 0.033 0.033
## 288 Im3 ~~ Im2 0.124 0.006 0.006 0.022 0.022
## 289 Im2 ~~ Im17 0.116 0.006 0.006 0.031 0.031
## 290 Im10 ~~ Im15 0.108 -0.005 -0.005 -0.018 -0.018
## 291 Im5 ~~ Im10 0.106 -0.006 -0.006 -0.018 -0.018
## 292 FRENCH =~ Im21 0.106 0.023 0.015 0.011 0.011
## 293 Im6 ~~ Im16 0.097 -0.014 -0.014 -0.014 -0.014
## 294 CHOICE =~ Im8 0.094 -0.009 -0.011 -0.010 -0.010
## 295 Im7 ~~ Im11 0.091 -0.012 -0.012 -0.014 -0.014
## 296 Im10 ~~ Im21 0.089 -0.005 -0.005 -0.018 -0.018
## 297 Im11 ~~ Im18 0.089 0.010 0.010 0.015 0.015
## 298 Im5 ~~ Im2 0.087 -0.008 -0.008 -0.016 -0.016
## 299 Im7 ~~ Im18 0.086 -0.010 -0.010 -0.015 -0.015
## 300 QUAL =~ Im6 0.086 -0.023 -0.016 -0.013 -0.013
## 301 Im5 ~~ Im12 0.084 0.008 0.008 0.017 0.017
## 302 CHOICE =~ Im11 0.082 -0.012 -0.015 -0.013 -0.013
## 303 Im8 ~~ Im12 0.076 -0.006 -0.006 -0.016 -0.016
## 304 Im6 ~~ Im13 0.071 0.009 0.009 0.014 0.014
## 305 Im14 ~~ Im20 0.068 -0.004 -0.004 -0.018 -0.018
## 306 Im5 ~~ Im7 0.064 0.010 0.010 0.012 0.012
## 307 Im22 ~~ Im17 0.054 0.006 0.006 0.022 0.022
## 308 Im6 ~~ Im21 0.052 -0.010 -0.010 -0.011 -0.011
## 309 QUAL =~ Im21 0.051 0.016 0.011 0.008 0.008
## 310 Im4 ~~ Im21 0.046 0.005 0.005 0.017 0.017
## 311 Im21 ~~ Im15 0.040 -0.007 -0.007 -0.010 -0.010
## 312 Im14 ~~ Im12 0.039 -0.003 -0.003 -0.015 -0.015
## 313 Im7 ~~ Im13 0.037 -0.006 -0.006 -0.011 -0.011
## 314 Im8 ~~ Im17 0.036 -0.004 -0.004 -0.015 -0.015
## 315 QUAL =~ Im17 0.035 -0.015 -0.011 -0.009 -0.009
## 316 BRAND =~ Im21 0.027 -0.007 -0.009 -0.006 -0.006
## 317 Im14 ~~ Im19 0.027 0.003 0.003 0.010 0.010
## 318 Im20 ~~ Im9 0.021 0.007 0.007 0.008 0.008
## 319 Im7 ~~ Im17 0.021 -0.004 -0.004 -0.011 -0.011
## 320 BRAND =~ Im8 0.020 0.004 0.005 0.005 0.005
## 321 CHOICE =~ Im3 0.018 -0.004 -0.004 -0.003 -0.003
## 322 Im3 ~~ Im9 0.018 -0.004 -0.004 -0.007 -0.007
## 323 Im5 ~~ Im18 0.017 0.004 0.004 0.007 0.007
## 324 DECO =~ Im21 0.017 0.005 0.006 0.005 0.005
## 325 Im8 ~~ Im20 0.014 0.003 0.003 0.006 0.006
## 326 Im4 ~~ Im9 0.014 -0.003 -0.003 -0.008 -0.008
## 327 Im3 ~~ Im21 0.010 -0.002 -0.002 -0.006 -0.006
## 328 ATMOS =~ Im18 0.009 0.004 0.005 0.004 0.004
## 329 Im11 ~~ Im15 0.007 -0.003 -0.003 -0.004 -0.004
## 330 Im7 ~~ Im2 0.006 -0.002 -0.002 -0.004 -0.004
## 331 FRENCH =~ Im12 0.002 -0.003 -0.002 -0.002 -0.002
## 332 Im13 ~~ Im9 0.002 0.002 0.002 0.003 0.003
## 333 Im4 ~~ Im14 0.002 0.000 0.000 -0.004 -0.004
## 334 Im4 ~~ Im7 0.002 -0.001 -0.001 -0.003 -0.003
## 335 Im8 ~~ Im11 0.002 0.001 0.001 0.002 0.002
## 336 Im13 ~~ Im19 0.002 0.001 0.001 0.002 0.002
## 337 Im3 ~~ Im6 0.002 0.001 0.001 0.002 0.002
## 338 Im22 ~~ Im16 0.001 0.001 0.001 0.002 0.002
## 339 QUAL =~ Im3 0.001 0.001 0.001 0.001 0.001
## 340 Im6 ~~ Im17 0.000 0.000 0.000 -0.001 -0.001
## 341 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
Based on the modification indices we create a new model
# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "
# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "
CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 85
##
## Number of observations 553
## Number of missing patterns 79
##
## Model Test User Model:
##
## Test statistic 259.047
## Degrees of freedom 124
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 7474.765
## Degrees of freedom 171
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.982
## Tucker-Lewis Index (TLI) 0.975
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.974
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12973.111
## Loglikelihood unrestricted model (H1) -12843.588
##
## Akaike (AIC) 26116.223
## Bayesian (BIC) 26483.028
## Sample-size adjusted Bayesian (SABIC) 26213.200
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.044
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.052
## P-value H_0: RMSEA <= 0.050 0.886
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.045
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.053
## P-value H_0: Robust RMSEA <= 0.050 0.825
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.937
## Im4 1.056 0.025 42.717 0.000 1.305 0.969
## Im5 0.818 0.034 23.815 0.000 1.011 0.760
## FOOD =~
## Im10 1.000 0.812 0.923
## Im14 1.015 0.036 28.479 0.000 0.824 0.952
## ATMOS =~
## Im20 1.000 1.265 0.845
## Im21 0.849 0.041 20.823 0.000 1.074 0.783
## Im22 1.060 0.047 22.606 0.000 1.340 0.877
## PRODQUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.046 0.000 0.991 0.872
## Im13 1.465 0.105 13.968 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.305 0.980
## Im2 0.885 0.033 27.043 0.000 1.155 0.899
## PROF =~
## Im16 1.000 0.921 0.766
## Im19 1.046 0.061 17.170 0.000 0.963 0.856
## BRAND =~
## Im17 1.000 1.204 0.969
## Im18 0.994 0.041 24.143 0.000 1.197 0.856
## FRENCH =~
## Im6 1.000 0.975 0.813
## Im7 1.184 0.071 16.770 0.000 1.155 0.955
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.418 0.050 8.393 0.000 0.416 0.416
## ATMOS 0.730 0.082 8.912 0.000 0.467 0.467
## PRODQUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.711 0.079 9.032 0.000 0.441 0.441
## PROF 0.743 0.071 10.465 0.000 0.653 0.653
## BRAND 0.770 0.076 10.140 0.000 0.517 0.517
## FRENCH 0.402 0.063 6.350 0.000 0.334 0.334
## FOOD ~~
## ATMOS 0.303 0.051 5.948 0.000 0.295 0.295
## PRODQUAL 0.258 0.034 7.662 0.000 0.452 0.452
## CHOICE 0.328 0.050 6.584 0.000 0.309 0.309
## PROF 0.372 0.043 8.589 0.000 0.498 0.498
## BRAND 0.318 0.047 6.801 0.000 0.325 0.325
## FRENCH 0.463 0.047 9.829 0.000 0.585 0.585
## ATMOS ~~
## PRODQUAL 0.372 0.053 7.011 0.000 0.418 0.418
## CHOICE 0.739 0.085 8.728 0.000 0.448 0.448
## PROF 0.557 0.069 8.089 0.000 0.478 0.478
## BRAND 0.787 0.081 9.715 0.000 0.516 0.516
## FRENCH 0.410 0.065 6.352 0.000 0.333 0.333
## PRODQUAL ~~
## CHOICE 0.439 0.054 8.161 0.000 0.478 0.478
## PROF 0.343 0.043 7.946 0.000 0.529 0.529
## BRAND 0.479 0.053 9.046 0.000 0.566 0.566
## FRENCH 0.210 0.037 5.622 0.000 0.306 0.306
## CHOICE ~~
## PROF 0.717 0.072 9.956 0.000 0.597 0.597
## BRAND 0.817 0.079 10.362 0.000 0.519 0.519
## FRENCH 0.286 0.060 4.735 0.000 0.225 0.225
## PROF ~~
## BRAND 0.667 0.066 10.040 0.000 0.601 0.601
## FRENCH 0.328 0.051 6.438 0.000 0.366 0.366
## BRAND ~~
## FRENCH 0.378 0.061 6.175 0.000 0.322 0.322
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.560 0.000 4.995 3.786
## .Im4 4.999 0.057 86.983 0.000 4.999 3.712
## .Im5 5.035 0.057 87.844 0.000 5.035 3.787
## .Im10 6.100 0.037 162.789 0.000 6.100 6.937
## .Im14 6.138 0.037 165.861 0.000 6.138 7.093
## .Im20 4.672 0.064 73.177 0.000 4.672 3.123
## .Im21 5.139 0.058 87.970 0.000 5.139 3.751
## .Im22 4.279 0.065 65.401 0.000 4.279 2.799
## .Im11 5.653 0.049 115.271 0.000 5.653 4.943
## .Im12 5.666 0.049 116.089 0.000 5.666 4.983
## .Im13 5.448 0.052 105.615 0.000 5.448 4.524
## .Im1 4.790 0.057 84.202 0.000 4.790 3.597
## .Im2 4.857 0.055 88.354 0.000 4.857 3.779
## .Im16 5.135 0.052 99.147 0.000 5.135 4.269
## .Im19 5.145 0.048 106.948 0.000 5.145 4.574
## .Im17 5.025 0.053 94.519 0.000 5.025 4.041
## .Im18 4.595 0.060 76.447 0.000 4.595 3.287
## .Im6 5.827 0.051 113.784 0.000 5.827 4.858
## .Im7 5.753 0.052 110.826 0.000 5.753 4.756
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.213 0.024 8.755 0.000 0.213 0.122
## .Im4 0.109 0.024 4.532 0.000 0.109 0.060
## .Im5 0.747 0.049 15.217 0.000 0.747 0.422
## .Im10 0.114 0.019 5.961 0.000 0.114 0.148
## .Im14 0.070 0.019 3.680 0.000 0.070 0.093
## .Im20 0.638 0.061 10.451 0.000 0.638 0.285
## .Im21 0.725 0.057 12.672 0.000 0.725 0.386
## .Im22 0.541 0.063 8.539 0.000 0.541 0.231
## .Im11 0.814 0.055 14.802 0.000 0.814 0.622
## .Im12 0.310 0.040 7.845 0.000 0.310 0.240
## .Im13 0.390 0.045 8.765 0.000 0.390 0.269
## .Im1 0.070 0.050 1.394 0.163 0.070 0.040
## .Im2 0.317 0.044 7.233 0.000 0.317 0.192
## .Im16 0.599 0.052 11.498 0.000 0.599 0.414
## .Im19 0.338 0.045 7.457 0.000 0.338 0.267
## .Im17 0.095 0.045 2.112 0.035 0.095 0.062
## .Im18 0.521 0.055 9.540 0.000 0.521 0.267
## .Im6 0.487 0.056 8.677 0.000 0.487 0.339
## .Im7 0.128 0.067 1.930 0.054 0.128 0.088
## DECO 1.528 0.107 14.326 0.000 1.000 1.000
## FOOD 0.659 0.049 13.328 0.000 1.000 1.000
## ATMOS 1.599 0.138 11.623 0.000 1.000 1.000
## PRODQUAL 0.494 0.067 7.361 0.000 1.000 1.000
## CHOICE 1.704 0.118 14.388 0.000 1.000 1.000
## PROF 0.849 0.088 9.638 0.000 1.000 1.000
## BRAND 1.451 0.104 13.988 0.000 1.000 1.000
## FRENCH 0.952 0.095 10.058 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1
## FOOD NaN 1
## ATMOS NaN NaN 1
## PRODQUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## PROF NaN NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN NaN 1
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH
## DECO 0.786707
## FOOD 0.786707
## ATMOS 0.786707
## PRODQUAL 0.786707
## CHOICE 0.786707
## PROF 0.786707
## BRAND 0.786707
## FRENCH 0.786707
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1.000
## FOOD 0.416 1.000
## ATMOS 0.467 0.295 1.000
## PRODQUAL 0.471 0.452 0.418 1.000
## CHOICE 0.441 0.309 0.448 0.478 1.000
## PROF 0.653 0.498 0.478 0.529 0.597 1.000
## BRAND 0.517 0.325 0.516 0.566 0.519 0.601 1.000
## FRENCH 0.334 0.585 0.333 0.306 0.225 0.366 0.322 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
arrange(modificationindices(CFA_fit_img_7f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 BRAND =~ Im13 23.832 0.220 0.265 0.220 0.220
## 2 Im11 ~~ Im13 21.323 -0.191 -0.191 -0.338 -0.338
## 3 BRAND =~ Im12 17.245 -0.179 -0.216 -0.190 -0.190
## 4 Im21 ~~ Im22 15.139 -0.285 -0.285 -0.455 -0.455
## 5 CHOICE =~ Im20 14.777 -0.151 -0.197 -0.132 -0.132
## 6 CHOICE =~ Im13 13.970 0.133 0.174 0.144 0.144
## 7 Im11 ~~ Im12 13.307 0.145 0.145 0.288 0.288
## 8 FOOD =~ Im11 12.742 0.215 0.174 0.152 0.152
## 9 Im20 ~~ Im21 11.455 0.228 0.228 0.335 0.335
## 10 ATMOS =~ Im12 10.952 -0.115 -0.145 -0.127 -0.127
## 11 Im13 ~~ Im1 10.707 0.068 0.068 0.409 0.409
## 12 CHOICE =~ Im12 10.663 -0.111 -0.145 -0.127 -0.127
## 13 Im13 ~~ Im17 9.392 0.068 0.068 0.355 0.355
## 14 Im4 ~~ Im17 9.096 -0.046 -0.046 -0.446 -0.446
## 15 BRAND =~ Im20 8.230 -0.133 -0.160 -0.107 -0.107
## 16 Im10 ~~ Im16 7.956 0.046 0.046 0.175 0.175
## 17 BRAND =~ Im22 7.656 0.131 0.158 0.103 0.103
## 18 FRENCH =~ Im22 7.278 0.136 0.132 0.087 0.087
## 19 ATMOS =~ Im11 6.691 0.101 0.128 0.112 0.112
## 20 Im22 ~~ Im12 6.644 -0.076 -0.076 -0.185 -0.185
## 21 CHOICE =~ Im5 6.302 0.086 0.112 0.084 0.084
## 22 BRAND =~ Im4 6.247 -0.067 -0.081 -0.060 -0.060
## 23 PRODQUAL =~ Im5 6.120 0.171 0.120 0.091 0.091
## 24 Im14 ~~ Im16 6.048 -0.039 -0.039 -0.191 -0.191
## 25 Im10 ~~ Im6 6.011 -0.035 -0.035 -0.147 -0.147
## 26 BRAND =~ Im5 5.755 0.095 0.115 0.086 0.086
## 27 Im3 ~~ Im1 5.614 -0.034 -0.034 -0.281 -0.281
## 28 DECO =~ Im7 5.531 -0.093 -0.114 -0.095 -0.095
## 29 DECO =~ Im6 5.531 0.078 0.097 0.080 0.080
## 30 ATMOS =~ Im5 5.517 0.089 0.113 0.085 0.085
## 31 DECO =~ Im18 5.361 0.099 0.123 0.088 0.088
## 32 DECO =~ Im17 5.361 -0.100 -0.124 -0.099 -0.099
## 33 FRENCH =~ Im20 5.231 -0.113 -0.111 -0.074 -0.074
## 34 Im22 ~~ Im11 5.182 0.087 0.087 0.131 0.131
## 35 FOOD =~ Im13 5.137 -0.127 -0.103 -0.086 -0.086
## 36 Im3 ~~ Im4 5.131 0.162 0.162 1.061 1.061
## 37 DECO =~ Im20 5.124 -0.096 -0.118 -0.079 -0.079
## 38 BRAND =~ Im7 5.064 -0.090 -0.108 -0.089 -0.089
## 39 BRAND =~ Im6 5.064 0.076 0.091 0.076 0.076
## 40 Im22 ~~ Im1 5.051 0.056 0.056 0.290 0.290
## 41 Im13 ~~ Im16 5.040 -0.067 -0.067 -0.138 -0.138
## 42 Im11 ~~ Im6 4.965 -0.069 -0.069 -0.109 -0.109
## 43 Im10 ~~ Im13 4.793 -0.031 -0.031 -0.146 -0.146
## 44 Im4 ~~ Im18 4.776 0.040 0.040 0.166 0.166
## 45 Im5 ~~ Im6 4.758 -0.065 -0.065 -0.108 -0.108
## 46 Im3 ~~ Im22 4.749 0.049 0.049 0.143 0.143
## 47 Im10 ~~ Im7 4.706 0.032 0.032 0.265 0.265
## 48 CHOICE =~ Im22 4.697 0.087 0.113 0.074 0.074
## 49 Im3 ~~ Im5 4.674 -0.071 -0.071 -0.178 -0.178
## 50 Im13 ~~ Im2 4.562 -0.044 -0.044 -0.125 -0.125
## 51 FOOD =~ Im5 4.520 0.117 0.095 0.072 0.072
## 52 Im20 ~~ Im17 4.488 -0.057 -0.057 -0.230 -0.230
## 53 ATMOS =~ Im4 4.309 -0.052 -0.066 -0.049 -0.049
## 54 DECO =~ Im22 4.302 0.090 0.111 0.072 0.072
## 55 PROF =~ Im2 4.223 0.170 0.157 0.122 0.122
## 56 PROF =~ Im1 4.223 -0.192 -0.177 -0.133 -0.133
## 57 Im20 ~~ Im6 4.215 -0.064 -0.064 -0.115 -0.115
## 58 PRODQUAL =~ Im1 4.027 0.145 0.102 0.077 0.077
## 59 PRODQUAL =~ Im2 4.027 -0.129 -0.090 -0.070 -0.070
## 60 PROF =~ Im12 3.965 -0.117 -0.108 -0.095 -0.095
## 61 Im14 ~~ Im6 3.823 0.027 0.027 0.149 0.149
## 62 FOOD =~ Im6 3.804 -0.271 -0.220 -0.183 -0.183
## 63 FOOD =~ Im7 3.804 0.321 0.260 0.215 0.215
## 64 Im2 ~~ Im17 3.691 0.033 0.033 0.192 0.192
## 65 Im4 ~~ Im6 3.588 0.033 0.033 0.143 0.143
## 66 Im3 ~~ Im17 3.342 0.028 0.028 0.198 0.198
## 67 Im11 ~~ Im1 3.335 -0.045 -0.045 -0.189 -0.189
## 68 Im5 ~~ Im1 3.275 0.043 0.043 0.188 0.188
## 69 PROF =~ Im20 3.209 -0.113 -0.104 -0.069 -0.069
## 70 CHOICE =~ Im21 3.202 0.067 0.087 0.064 0.064
## 71 Im3 ~~ Im2 3.151 0.026 0.026 0.100 0.100
## 72 Im20 ~~ Im13 3.089 0.055 0.055 0.111 0.111
## 73 Im18 ~~ Im6 3.067 0.046 0.046 0.091 0.091
## 74 Im14 ~~ Im7 3.014 -0.026 -0.026 -0.272 -0.272
## 75 Im11 ~~ Im17 2.983 -0.045 -0.045 -0.163 -0.163
## 76 FRENCH =~ Im11 2.967 0.080 0.078 0.069 0.069
## 77 ATMOS =~ Im13 2.904 0.062 0.078 0.065 0.065
## 78 Im5 ~~ Im7 2.807 0.048 0.048 0.154 0.154
## 79 Im10 ~~ Im11 2.784 0.028 0.028 0.093 0.093
## 80 Im20 ~~ Im1 2.774 -0.042 -0.042 -0.198 -0.198
## 81 Im5 ~~ Im14 2.721 0.026 0.026 0.115 0.115
## 82 Im1 ~~ Im17 2.656 -0.029 -0.029 -0.359 -0.359
## 83 FRENCH =~ Im19 2.578 0.085 0.083 0.074 0.074
## 84 FRENCH =~ Im16 2.578 -0.082 -0.080 -0.066 -0.066
## 85 Im2 ~~ Im16 2.577 0.038 0.038 0.088 0.088
## 86 CHOICE =~ Im14 2.577 0.027 0.035 0.041 0.041
## 87 CHOICE =~ Im10 2.577 -0.026 -0.035 -0.039 -0.039
## 88 Im21 ~~ Im18 2.573 -0.052 -0.052 -0.084 -0.084
## 89 Im4 ~~ Im11 2.457 -0.034 -0.034 -0.113 -0.113
## 90 PROF =~ Im13 2.455 0.096 0.089 0.074 0.074
## 91 Im22 ~~ Im19 2.419 -0.049 -0.049 -0.115 -0.115
## 92 Im4 ~~ Im22 2.418 -0.034 -0.034 -0.138 -0.138
## 93 Im3 ~~ Im20 2.350 -0.034 -0.034 -0.093 -0.093
## 94 Im12 ~~ Im7 2.333 0.036 0.036 0.178 0.178
## 95 DECO =~ Im12 2.244 -0.054 -0.066 -0.058 -0.058
## 96 Im11 ~~ Im7 2.221 0.044 0.044 0.137 0.137
## 97 Im19 ~~ Im17 2.187 0.035 0.035 0.193 0.193
## 98 PRODQUAL =~ Im16 2.157 -0.133 -0.094 -0.078 -0.078
## 99 PRODQUAL =~ Im19 2.157 0.140 0.098 0.087 0.087
## 100 Im10 ~~ Im17 2.035 -0.017 -0.017 -0.161 -0.161
## 101 Im14 ~~ Im17 1.988 0.016 0.016 0.201 0.201
## 102 Im4 ~~ Im1 1.978 0.020 0.020 0.227 0.227
## 103 Im3 ~~ Im12 1.906 -0.024 -0.024 -0.092 -0.092
## 104 Im12 ~~ Im6 1.902 -0.033 -0.033 -0.084 -0.084
## 105 CHOICE =~ Im16 1.817 0.068 0.089 0.074 0.074
## 106 CHOICE =~ Im19 1.817 -0.071 -0.093 -0.083 -0.083
## 107 Im14 ~~ Im2 1.800 0.015 0.015 0.098 0.098
## 108 Im18 ~~ Im7 1.743 -0.033 -0.033 -0.128 -0.128
## 109 FRENCH =~ Im5 1.735 0.059 0.057 0.043 0.043
## 110 Im11 ~~ Im2 1.713 0.033 0.033 0.064 0.064
## 111 ATMOS =~ Im17 1.684 -0.057 -0.073 -0.058 -0.058
## 112 ATMOS =~ Im18 1.684 0.057 0.072 0.052 0.052
## 113 Im19 ~~ Im18 1.680 -0.034 -0.034 -0.082 -0.082
## 114 BRAND =~ Im3 1.663 0.034 0.041 0.031 0.031
## 115 Im3 ~~ Im14 1.662 -0.012 -0.012 -0.102 -0.102
## 116 FRENCH =~ Im2 1.647 0.039 0.038 0.030 0.030
## 117 FRENCH =~ Im1 1.647 -0.045 -0.043 -0.033 -0.033
## 118 Im22 ~~ Im2 1.646 -0.032 -0.032 -0.077 -0.077
## 119 Im22 ~~ Im18 1.613 0.041 0.041 0.077 0.077
## 120 FOOD =~ Im2 1.604 0.050 0.040 0.031 0.031
## 121 FOOD =~ Im1 1.604 -0.056 -0.046 -0.034 -0.034
## 122 PRODQUAL =~ Im4 1.602 -0.058 -0.041 -0.030 -0.030
## 123 Im22 ~~ Im13 1.588 -0.040 -0.040 -0.086 -0.086
## 124 Im4 ~~ Im2 1.557 -0.018 -0.018 -0.095 -0.095
## 125 Im14 ~~ Im21 1.552 0.021 0.021 0.091 0.091
## 126 Im5 ~~ Im16 1.529 -0.043 -0.043 -0.064 -0.064
## 127 Im12 ~~ Im17 1.526 -0.026 -0.026 -0.151 -0.151
## 128 Im10 ~~ Im18 1.519 0.018 0.018 0.072 0.072
## 129 PRODQUAL =~ Im22 1.519 -0.095 -0.067 -0.044 -0.044
## 130 Im2 ~~ Im18 1.481 -0.026 -0.026 -0.063 -0.063
## 131 Im12 ~~ Im13 1.475 0.089 0.089 0.257 0.257
## 132 PRODQUAL =~ Im6 1.473 -0.073 -0.052 -0.043 -0.043
## 133 PRODQUAL =~ Im7 1.473 0.087 0.061 0.051 0.051
## 134 Im14 ~~ Im18 1.464 -0.017 -0.017 -0.088 -0.088
## 135 PROF =~ Im22 1.445 0.077 0.071 0.047 0.047
## 136 DECO =~ Im13 1.431 0.045 0.055 0.046 0.046
## 137 PRODQUAL =~ Im17 1.422 0.109 0.076 0.062 0.062
## 138 PRODQUAL =~ Im18 1.422 -0.108 -0.076 -0.054 -0.054
## 139 Im4 ~~ Im12 1.373 0.019 0.019 0.106 0.106
## 140 ATMOS =~ Im1 1.355 0.043 0.054 0.040 0.040
## 141 ATMOS =~ Im2 1.355 -0.038 -0.048 -0.037 -0.037
## 142 Im22 ~~ Im7 1.342 0.035 0.035 0.133 0.133
## 143 Im3 ~~ Im18 1.316 -0.022 -0.022 -0.065 -0.065
## 144 Im3 ~~ Im11 1.290 0.025 0.025 0.061 0.061
## 145 PROF =~ Im4 1.267 -0.055 -0.050 -0.037 -0.037
## 146 Im13 ~~ Im19 1.244 0.029 0.029 0.080 0.080
## 147 Im3 ~~ Im10 1.231 0.011 0.011 0.071 0.071
## 148 Im10 ~~ Im12 1.205 0.014 0.014 0.077 0.077
## 149 Im12 ~~ Im16 1.199 0.030 0.030 0.071 0.071
## 150 BRAND =~ Im11 1.070 -0.047 -0.056 -0.049 -0.049
## 151 BRAND =~ Im2 1.067 0.042 0.051 0.039 0.039
## 152 BRAND =~ Im1 1.067 -0.048 -0.057 -0.043 -0.043
## 153 Im14 ~~ Im12 1.061 -0.013 -0.013 -0.090 -0.090
## 154 Im4 ~~ Im7 1.054 -0.017 -0.017 -0.147 -0.147
## 155 PRODQUAL =~ Im20 1.037 0.077 0.054 0.036 0.036
## 156 Im21 ~~ Im17 1.017 0.027 0.027 0.101 0.101
## 157 Im20 ~~ Im19 0.988 0.031 0.031 0.068 0.068
## 158 PROF =~ Im17 0.986 0.084 0.077 0.062 0.062
## 159 PROF =~ Im18 0.986 -0.083 -0.077 -0.055 -0.055
## 160 Im19 ~~ Im7 0.949 0.025 0.025 0.122 0.122
## 161 PROF =~ Im7 0.940 -0.060 -0.055 -0.045 -0.045
## 162 PROF =~ Im6 0.940 0.050 0.046 0.039 0.039
## 163 Im13 ~~ Im18 0.925 -0.026 -0.026 -0.057 -0.057
## 164 Im5 ~~ Im2 0.918 -0.023 -0.023 -0.047 -0.047
## 165 Im14 ~~ Im13 0.889 0.013 0.013 0.079 0.079
## 166 Im16 ~~ Im7 0.880 -0.027 -0.027 -0.097 -0.097
## 167 Im1 ~~ Im18 0.847 0.019 0.019 0.101 0.101
## 168 ATMOS =~ Im3 0.826 0.022 0.028 0.022 0.022
## 169 FOOD =~ Im20 0.814 -0.052 -0.042 -0.028 -0.028
## 170 Im22 ~~ Im6 0.806 0.028 0.028 0.054 0.054
## 171 Im5 ~~ Im19 0.786 -0.026 -0.026 -0.052 -0.052
## 172 BRAND =~ Im16 0.775 -0.050 -0.060 -0.050 -0.050
## 173 BRAND =~ Im19 0.775 0.052 0.063 0.056 0.056
## 174 Im3 ~~ Im19 0.774 0.016 0.016 0.061 0.061
## 175 BRAND =~ Im14 0.773 0.017 0.020 0.023 0.023
## 176 BRAND =~ Im10 0.773 -0.016 -0.020 -0.022 -0.022
## 177 Im10 ~~ Im19 0.726 -0.012 -0.012 -0.062 -0.062
## 178 FRENCH =~ Im13 0.706 -0.035 -0.034 -0.028 -0.028
## 179 PROF =~ Im5 0.688 0.055 0.051 0.038 0.038
## 180 Im4 ~~ Im5 0.687 0.029 0.029 0.103 0.103
## 181 Im20 ~~ Im12 0.675 0.024 0.024 0.054 0.054
## 182 Im2 ~~ Im7 0.669 0.016 0.016 0.079 0.079
## 183 Im3 ~~ Im7 0.637 -0.014 -0.014 -0.084 -0.084
## 184 PRODQUAL =~ Im14 0.619 0.031 0.022 0.025 0.025
## 185 PRODQUAL =~ Im10 0.619 -0.030 -0.021 -0.024 -0.024
## 186 Im21 ~~ Im7 0.611 -0.023 -0.023 -0.076 -0.076
## 187 Im5 ~~ Im22 0.596 0.028 0.028 0.044 0.044
## 188 Im4 ~~ Im10 0.595 -0.007 -0.007 -0.066 -0.066
## 189 Im20 ~~ Im18 0.582 0.025 0.025 0.043 0.043
## 190 Im10 ~~ Im2 0.581 -0.008 -0.008 -0.045 -0.045
## 191 Im4 ~~ Im16 0.579 0.016 0.016 0.062 0.062
## 192 Im21 ~~ Im2 0.574 0.019 0.019 0.039 0.039
## 193 Im10 ~~ Im21 0.544 -0.013 -0.013 -0.043 -0.043
## 194 Im14 ~~ Im22 0.525 -0.012 -0.012 -0.062 -0.062
## 195 Im13 ~~ Im7 0.518 -0.018 -0.018 -0.080 -0.080
## 196 Im5 ~~ Im11 0.501 0.026 0.026 0.033 0.033
## 197 Im20 ~~ Im11 0.498 0.027 0.027 0.038 0.038
## 198 Im12 ~~ Im2 0.492 -0.013 -0.013 -0.043 -0.043
## 199 Im11 ~~ Im18 0.492 0.023 0.023 0.035 0.035
## 200 CHOICE =~ Im3 0.483 -0.015 -0.020 -0.015 -0.015
## 201 Im1 ~~ Im16 0.483 -0.017 -0.017 -0.082 -0.082
## 202 Im21 ~~ Im12 0.479 0.020 0.020 0.043 0.043
## 203 Im5 ~~ Im10 0.474 -0.011 -0.011 -0.039 -0.039
## 204 CHOICE =~ Im11 0.473 -0.026 -0.034 -0.030 -0.030
## 205 Im10 ~~ Im20 0.466 0.012 0.012 0.043 0.043
## 206 PROF =~ Im3 0.453 0.032 0.029 0.022 0.022
## 207 FRENCH =~ Im3 0.431 -0.019 -0.018 -0.014 -0.014
## 208 FOOD =~ Im3 0.430 -0.023 -0.019 -0.014 -0.014
## 209 FOOD =~ Im19 0.429 0.047 0.038 0.034 0.034
## 210 FOOD =~ Im16 0.429 -0.045 -0.037 -0.031 -0.031
## 211 PROF =~ Im11 0.410 0.039 0.036 0.032 0.032
## 212 Im5 ~~ Im20 0.382 0.023 0.023 0.033 0.033
## 213 Im13 ~~ Im6 0.377 0.016 0.016 0.036 0.036
## 214 Im14 ~~ Im19 0.372 0.009 0.009 0.056 0.056
## 215 Im21 ~~ Im13 0.372 -0.019 -0.019 -0.036 -0.036
## 216 PROF =~ Im21 0.371 0.036 0.033 0.024 0.024
## 217 CHOICE =~ Im4 0.369 -0.014 -0.018 -0.013 -0.013
## 218 Im22 ~~ Im17 0.360 0.016 0.016 0.071 0.071
## 219 FRENCH =~ Im21 0.360 -0.029 -0.028 -0.020 -0.020
## 220 Im21 ~~ Im11 0.346 -0.022 -0.022 -0.029 -0.029
## 221 Im5 ~~ Im17 0.345 0.015 0.015 0.055 0.055
## 222 Im14 ~~ Im20 0.330 -0.010 -0.010 -0.045 -0.045
## 223 FOOD =~ Im21 0.320 0.032 0.026 0.019 0.019
## 224 CHOICE =~ Im17 0.309 0.023 0.030 0.024 0.024
## 225 CHOICE =~ Im18 0.309 -0.023 -0.030 -0.021 -0.021
## 226 Im3 ~~ Im13 0.299 0.010 0.010 0.035 0.035
## 227 Im4 ~~ Im19 0.281 -0.010 -0.010 -0.050 -0.050
## 228 Im22 ~~ Im16 0.277 0.019 0.019 0.033 0.033
## 229 Im5 ~~ Im21 0.277 -0.019 -0.019 -0.026 -0.026
## 230 Im4 ~~ Im14 0.246 0.005 0.005 0.053 0.053
## 231 DECO =~ Im11 0.238 0.019 0.024 0.021 0.021
## 232 Im16 ~~ Im18 0.231 -0.015 -0.015 -0.026 -0.026
## 233 Im17 ~~ Im7 0.228 -0.010 -0.010 -0.094 -0.094
## 234 Im21 ~~ Im16 0.227 -0.017 -0.017 -0.026 -0.026
## 235 Im20 ~~ Im22 0.211 0.043 0.043 0.074 0.074
## 236 Im17 ~~ Im6 0.208 0.010 0.010 0.045 0.045
## 237 Im20 ~~ Im2 0.203 -0.011 -0.011 -0.025 -0.025
## 238 Im2 ~~ Im19 0.202 -0.009 -0.009 -0.029 -0.029
## 239 FOOD =~ Im4 0.194 -0.016 -0.013 -0.010 -0.010
## 240 Im4 ~~ Im13 0.168 -0.007 -0.007 -0.035 -0.035
## 241 Im14 ~~ Im11 0.165 0.007 0.007 0.028 0.028
## 242 FOOD =~ Im22 0.151 0.023 0.018 0.012 0.012
## 243 Im12 ~~ Im18 0.146 -0.010 -0.010 -0.024 -0.024
## 244 Im20 ~~ Im16 0.145 0.014 0.014 0.022 0.022
## 245 Im21 ~~ Im1 0.132 0.009 0.009 0.040 0.040
## 246 ATMOS =~ Im19 0.131 -0.017 -0.022 -0.019 -0.019
## 247 ATMOS =~ Im16 0.131 0.016 0.021 0.017 0.017
## 248 Im4 ~~ Im20 0.129 0.008 0.008 0.029 0.029
## 249 Im1 ~~ Im7 0.126 -0.007 -0.007 -0.075 -0.075
## 250 Im12 ~~ Im1 0.110 -0.006 -0.006 -0.044 -0.044
## 251 Im3 ~~ Im6 0.106 0.006 0.006 0.018 0.018
## 252 Im2 ~~ Im6 0.094 -0.006 -0.006 -0.016 -0.016
## 253 FRENCH =~ Im18 0.094 0.013 0.012 0.009 0.009
## 254 FRENCH =~ Im17 0.094 -0.013 -0.013 -0.010 -0.010
## 255 Im10 ~~ Im1 0.093 -0.003 -0.003 -0.038 -0.038
## 256 PRODQUAL =~ Im21 0.088 0.021 0.015 0.011 0.011
## 257 Im5 ~~ Im18 0.083 0.009 0.009 0.014 0.014
## 258 Im20 ~~ Im7 0.082 0.009 0.009 0.030 0.030
## 259 DECO =~ Im2 0.075 0.009 0.011 0.008 0.008
## 260 DECO =~ Im1 0.075 -0.010 -0.012 -0.009 -0.009
## 261 Im5 ~~ Im12 0.067 0.007 0.007 0.015 0.015
## 262 Im14 ~~ Im1 0.063 -0.003 -0.003 -0.039 -0.039
## 263 ATMOS =~ Im14 0.061 0.004 0.006 0.006 0.006
## 264 ATMOS =~ Im10 0.061 -0.004 -0.006 -0.006 -0.006
## 265 Im21 ~~ Im19 0.060 0.008 0.008 0.015 0.015
## 266 Im4 ~~ Im21 0.059 0.005 0.005 0.018 0.018
## 267 PROF =~ Im10 0.058 0.008 0.007 0.008 0.008
## 268 PROF =~ Im14 0.058 -0.008 -0.007 -0.009 -0.009
## 269 Im1 ~~ Im19 0.056 -0.005 -0.005 -0.034 -0.034
## 270 CHOICE =~ Im6 0.055 -0.007 -0.009 -0.007 -0.007
## 271 CHOICE =~ Im7 0.055 0.008 0.010 0.008 0.008
## 272 DECO =~ Im14 0.052 0.005 0.006 0.007 0.007
## 273 DECO =~ Im10 0.052 -0.005 -0.006 -0.006 -0.006
## 274 Im10 ~~ Im22 0.051 0.004 0.004 0.015 0.015
## 275 FRENCH =~ Im12 0.045 -0.008 -0.008 -0.007 -0.007
## 276 Im1 ~~ Im6 0.039 -0.004 -0.004 -0.021 -0.021
## 277 ATMOS =~ Im6 0.036 -0.006 -0.008 -0.007 -0.007
## 278 ATMOS =~ Im7 0.036 0.008 0.010 0.008 0.008
## 279 Im12 ~~ Im19 0.023 -0.004 -0.004 -0.011 -0.011
## 280 DECO =~ Im21 0.016 0.005 0.006 0.005 0.005
## 281 FOOD =~ Im17 0.015 0.006 0.005 0.004 0.004
## 282 FOOD =~ Im18 0.015 -0.006 -0.005 -0.004 -0.004
## 283 Im3 ~~ Im21 0.013 -0.003 -0.003 -0.006 -0.006
## 284 Im16 ~~ Im6 0.011 -0.003 -0.003 -0.006 -0.006
## 285 Im19 ~~ Im6 0.009 -0.002 -0.002 -0.006 -0.006
## 286 Im11 ~~ Im19 0.006 -0.002 -0.002 -0.005 -0.005
## 287 Im21 ~~ Im6 0.006 0.002 0.002 0.004 0.004
## 288 DECO =~ Im16 0.004 0.004 0.005 0.004 0.004
## 289 DECO =~ Im19 0.004 -0.004 -0.005 -0.004 -0.004
## 290 Im11 ~~ Im16 0.002 0.002 0.002 0.002 0.002
## 291 FRENCH =~ Im14 0.001 0.001 0.001 0.002 0.002
## 292 FRENCH =~ Im10 0.001 -0.001 -0.001 -0.002 -0.002
## 293 Im3 ~~ Im16 0.001 -0.001 -0.001 -0.002 -0.002
## 294 FRENCH =~ Im4 0.001 -0.001 -0.001 0.000 0.000
## 295 Im16 ~~ Im17 0.000 0.000 0.000 0.002 0.002
## 296 PRODQUAL =~ Im3 0.000 0.000 0.000 0.000 0.000
## 297 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
## 298 BRAND =~ Im21 0.000 0.000 0.000 0.000 0.000
## 299 FOOD =~ Im12 0.000 0.000 0.000 0.000 0.000
## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
#
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
#
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
#
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
#
# CFA_data# missing Im8, Im15, Im9
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "
# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4
SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
"# # linear regression
# lm_SAT_1 <- lm (model_SAT_1, data = survey)
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 143 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 148
##
## Number of observations 553
## Number of missing patterns 135
##
## Model Test User Model:
##
## Test statistic 807.817
## Degrees of freedom 412
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11978.557
## Degrees of freedom 496
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.966
## Tucker-Lewis Index (TLI) 0.959
##
## Robust Comparative Fit Index (CFI) 0.966
## Robust Tucker-Lewis Index (TLI) 0.959
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -22422.581
## Loglikelihood unrestricted model (H1) -22018.673
##
## Akaike (AIC) 45141.162
## Bayesian (BIC) 45779.835
## Sample-size adjusted Bayesian (SABIC) 45310.018
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.042
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.046
## P-value H_0: RMSEA <= 0.050 0.999
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.042
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.047
## P-value H_0: Robust RMSEA <= 0.050 0.998
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.059
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.235 0.936
## Im4 1.057 0.025 42.676 0.000 1.306 0.970
## Im5 0.818 0.034 23.801 0.000 1.010 0.760
## FOOD =~
## Im10 1.000 0.810 0.921
## Im14 1.019 0.036 28.596 0.000 0.826 0.954
## ATMOS =~
## Im20 1.000 1.253 0.838
## Im21 0.865 0.041 20.940 0.000 1.084 0.791
## Im22 1.060 0.046 23.188 0.000 1.327 0.869
## PRODQUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.409 0.094 15.045 0.000 0.991 0.872
## Im13 1.464 0.105 13.957 0.000 1.029 0.855
## CHOICE =~
## Im1 1.000 1.302 0.978
## Im2 0.889 0.032 27.907 0.000 1.157 0.900
## PROF =~
## Im16 1.000 0.911 0.757
## Im19 1.030 0.056 18.278 0.000 0.938 0.834
## BRAND =~
## Im17 1.000 1.205 0.970
## Im18 0.992 0.041 24.147 0.000 1.196 0.856
## FRENCH =~
## Im6 1.000 0.986 0.822
## Im7 1.161 0.066 17.619 0.000 1.144 0.945
## AFCOM =~
## COM_A1 1.000 1.120 0.785
## COM_A2 1.180 0.056 21.211 0.000 1.321 0.830
## COM_A3 1.176 0.059 19.829 0.000 1.317 0.816
## COM_A4 1.297 0.063 20.613 0.000 1.453 0.845
## SAT =~
## SAT_1 1.000 0.868 0.859
## SAT_2 0.937 0.049 19.036 0.000 0.814 0.818
## SAT_3 0.812 0.055 14.799 0.000 0.705 0.620
## RI =~
## C_REP1 1.000 0.588 0.798
## C_REP2 1.021 0.047 21.905 0.000 0.601 0.955
## C_REP3 0.719 0.038 19.135 0.000 0.423 0.758
## COI =~
## C_CR1 1.000 1.641 0.848
## C_CR3 1.033 0.051 20.134 0.000 1.695 0.822
## C_CR4 0.967 0.049 19.687 0.000 1.587 0.805
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SAT ~
## DECO -0.107 0.046 -2.357 0.018 -0.153 -0.153
## CHOICE 0.095 0.040 2.379 0.017 0.142 0.142
## PROF 0.615 0.090 6.808 0.000 0.645 0.645
## AFCOM ~
## ATMOS 0.437 0.047 9.282 0.000 0.489 0.489
## PRODQUAL -0.037 0.076 -0.485 0.628 -0.023 -0.023
## FRENCH 0.206 0.051 4.031 0.000 0.182 0.182
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.416 0.050 8.380 0.000 0.416 0.416
## ATMOS 0.730 0.081 8.972 0.000 0.472 0.472
## PRODQUAL 0.408 0.051 8.031 0.000 0.470 0.470
## CHOICE 0.709 0.079 9.024 0.000 0.441 0.441
## PROF 0.750 0.070 10.690 0.000 0.667 0.667
## BRAND 0.768 0.076 10.124 0.000 0.516 0.516
## FRENCH 0.412 0.063 6.494 0.000 0.338 0.338
## RI 0.181 0.035 5.193 0.000 0.249 0.249
## COI 0.047 0.095 0.492 0.623 0.023 0.023
## FOOD ~~
## ATMOS 0.303 0.050 6.019 0.000 0.299 0.299
## PRODQUAL 0.257 0.034 7.652 0.000 0.452 0.452
## CHOICE 0.328 0.050 6.606 0.000 0.311 0.311
## PROF 0.387 0.043 8.999 0.000 0.525 0.525
## BRAND 0.317 0.047 6.798 0.000 0.325 0.325
## FRENCH 0.469 0.047 10.016 0.000 0.588 0.588
## RI 0.123 0.023 5.283 0.000 0.258 0.258
## COI -0.044 0.063 -0.700 0.484 -0.033 -0.033
## ATMOS ~~
## PRODQUAL 0.370 0.053 7.026 0.000 0.420 0.420
## CHOICE 0.748 0.084 8.879 0.000 0.458 0.458
## PROF 0.580 0.068 8.542 0.000 0.508 0.508
## BRAND 0.785 0.080 9.748 0.000 0.520 0.520
## FRENCH 0.411 0.065 6.374 0.000 0.333 0.333
## RI 0.281 0.040 7.034 0.000 0.381 0.381
## COI 0.436 0.103 4.210 0.000 0.212 0.212
## PRODQUAL ~~
## CHOICE 0.437 0.054 8.146 0.000 0.477 0.477
## PROF 0.348 0.043 8.092 0.000 0.543 0.543
## BRAND 0.479 0.053 9.046 0.000 0.566 0.566
## FRENCH 0.211 0.038 5.621 0.000 0.305 0.305
## RI 0.112 0.022 5.128 0.000 0.270 0.270
## COI 0.060 0.058 1.036 0.300 0.052 0.052
## CHOICE ~~
## PROF 0.725 0.071 10.200 0.000 0.611 0.611
## BRAND 0.816 0.079 10.366 0.000 0.520 0.520
## FRENCH 0.296 0.061 4.829 0.000 0.231 0.231
## RI 0.216 0.037 5.829 0.000 0.282 0.282
## COI 0.068 0.100 0.678 0.498 0.032 0.032
## PROF ~~
## BRAND 0.676 0.065 10.326 0.000 0.616 0.616
## FRENCH 0.363 0.052 6.990 0.000 0.404 0.404
## RI 0.200 0.030 6.678 0.000 0.373 0.373
## COI -0.079 0.077 -1.029 0.304 -0.053 -0.053
## BRAND ~~
## FRENCH 0.388 0.061 6.333 0.000 0.327 0.327
## RI 0.188 0.034 5.501 0.000 0.265 0.265
## COI 0.111 0.094 1.190 0.234 0.056 0.056
## FRENCH ~~
## RI 0.134 0.029 4.535 0.000 0.230 0.230
## COI 0.004 0.078 0.051 0.959 0.002 0.002
## RI ~~
## COI 0.078 0.047 1.677 0.094 0.081 0.081
## .AFCOM ~~
## .SAT 0.218 0.037 5.825 0.000 0.357 0.357
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.576 0.000 4.995 3.787
## .Im4 4.999 0.057 86.999 0.000 4.999 3.713
## .Im5 5.036 0.057 87.853 0.000 5.036 3.787
## .Im10 6.100 0.037 162.781 0.000 6.100 6.936
## .Im14 6.138 0.037 165.851 0.000 6.138 7.093
## .Im20 4.672 0.064 73.228 0.000 4.672 3.125
## .Im21 5.139 0.058 87.975 0.000 5.139 3.750
## .Im22 4.280 0.065 65.485 0.000 4.280 2.802
## .Im11 5.654 0.049 115.283 0.000 5.654 4.943
## .Im12 5.666 0.049 116.116 0.000 5.666 4.985
## .Im13 5.448 0.052 105.654 0.000 5.448 4.526
## .Im1 4.792 0.057 84.287 0.000 4.792 3.600
## .Im2 4.858 0.055 88.415 0.000 4.858 3.781
## .Im16 5.135 0.052 99.179 0.000 5.135 4.269
## .Im19 5.146 0.048 107.001 0.000 5.146 4.575
## .Im17 5.025 0.053 94.560 0.000 5.025 4.043
## .Im18 4.595 0.060 76.466 0.000 4.595 3.288
## .Im6 5.827 0.051 113.792 0.000 5.827 4.858
## .Im7 5.753 0.052 110.790 0.000 5.753 4.754
## .COM_A1 4.287 0.061 70.288 0.000 4.287 3.007
## .COM_A2 3.887 0.068 57.199 0.000 3.887 2.443
## .COM_A3 3.542 0.069 51.223 0.000 3.542 2.194
## .COM_A4 3.458 0.073 47.108 0.000 3.458 2.010
## .SAT_1 5.343 0.043 124.118 0.000 5.343 5.289
## .SAT_2 5.483 0.042 129.018 0.000 5.483 5.510
## .SAT_3 5.458 0.050 109.971 0.000 5.458 4.798
## .C_REP1 4.283 0.031 136.277 0.000 4.283 5.807
## .C_REP2 4.507 0.027 167.674 0.000 4.507 7.164
## .C_REP3 4.676 0.024 195.449 0.000 4.676 8.380
## .C_CR1 2.679 0.083 32.285 0.000 2.679 1.384
## .C_CR3 3.261 0.088 37.105 0.000 3.261 1.582
## .C_CR4 2.786 0.084 33.092 0.000 2.786 1.414
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## .AFCOM 0.000 0.000 0.000
## .SAT 0.000 0.000 0.000
## RI 0.000 0.000 0.000
## COI 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.214 0.024 8.767 0.000 0.214 0.123
## .Im4 0.108 0.024 4.461 0.000 0.108 0.059
## .Im5 0.747 0.049 15.220 0.000 0.747 0.423
## .Im10 0.117 0.019 6.135 0.000 0.117 0.151
## .Im14 0.067 0.019 3.559 0.000 0.067 0.089
## .Im20 0.666 0.059 11.280 0.000 0.666 0.298
## .Im21 0.703 0.055 12.679 0.000 0.703 0.374
## .Im22 0.571 0.060 9.496 0.000 0.571 0.245
## .Im11 0.814 0.055 14.788 0.000 0.814 0.622
## .Im12 0.310 0.040 7.841 0.000 0.310 0.240
## .Im13 0.390 0.045 8.730 0.000 0.390 0.269
## .Im1 0.076 0.048 1.598 0.110 0.076 0.043
## .Im2 0.312 0.042 7.417 0.000 0.312 0.189
## .Im16 0.618 0.051 12.116 0.000 0.618 0.427
## .Im19 0.385 0.045 8.653 0.000 0.385 0.304
## .Im17 0.093 0.045 2.055 0.040 0.093 0.060
## .Im18 0.524 0.055 9.587 0.000 0.524 0.268
## .Im6 0.468 0.054 8.714 0.000 0.468 0.325
## .Im7 0.155 0.062 2.520 0.012 0.155 0.106
## .COM_A1 0.779 0.060 13.036 0.000 0.779 0.383
## .COM_A2 0.787 0.067 11.838 0.000 0.787 0.311
## .COM_A3 0.872 0.070 12.387 0.000 0.872 0.335
## .COM_A4 0.849 0.075 11.385 0.000 0.849 0.287
## .SAT_1 0.267 0.034 7.920 0.000 0.267 0.262
## .SAT_2 0.328 0.033 9.901 0.000 0.328 0.331
## .SAT_3 0.797 0.056 14.318 0.000 0.797 0.616
## .C_REP1 0.198 0.016 12.178 0.000 0.198 0.364
## .C_REP2 0.035 0.011 3.224 0.001 0.035 0.089
## .C_REP3 0.133 0.009 14.064 0.000 0.133 0.426
## .C_CR1 1.054 0.114 9.275 0.000 1.054 0.281
## .C_CR3 1.375 0.131 10.514 0.000 1.375 0.324
## .C_CR4 1.366 0.123 11.130 0.000 1.366 0.352
## DECO 1.526 0.107 14.317 0.000 1.000 1.000
## FOOD 0.657 0.049 13.302 0.000 1.000 1.000
## ATMOS 1.569 0.135 11.580 0.000 1.000 1.000
## PRODQUAL 0.494 0.067 7.362 0.000 1.000 1.000
## CHOICE 1.696 0.117 14.476 0.000 1.000 1.000
## PROF 0.829 0.086 9.605 0.000 1.000 1.000
## BRAND 1.452 0.104 14.014 0.000 1.000 1.000
## FRENCH 0.971 0.094 10.349 0.000 1.000 1.000
## .AFCOM 0.854 0.086 9.878 0.000 0.681 0.681
## .SAT 0.436 0.050 8.755 0.000 0.579 0.579
## RI 0.346 0.032 10.668 0.000 1.000 1.000
## COI 2.693 0.238 11.334 0.000 1.000 1.000
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN NaN NaN NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_3 NaN NaN NaN NaN NaN NaN NaN NaN NaN 0.384 NaN NaN
## C_REP1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO 1
## FOOD NaN 1
## ATMOS NaN NaN 1
## PRODQUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## PROF NaN NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN NaN 1
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FOOD 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## ATMOS 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PRODQUAL 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## CHOICE 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PROF 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## BRAND 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## AFCOM 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## SAT 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## RI 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## COI 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH AFCOM SAT RI COI
## DECO 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FOOD 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## ATMOS 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PRODQUAL 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## CHOICE 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PROF 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## BRAND 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FRENCH 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## AFCOM 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## SAT 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## RI 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## COI 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO 1.000
## FOOD 0.416 1.000
## ATMOS 0.472 0.299 1.000
## PRODQUAL 0.470 0.452 0.420 1.000
## CHOICE 0.441 0.311 0.458 0.477 1.000
## PROF 0.667 0.525 0.508 0.543 0.611 1.000
## BRAND 0.516 0.325 0.520 0.566 0.520 0.616 1.000
## FRENCH 0.338 0.588 0.333 0.305 0.231 0.404 0.327 1.000
## AFCOM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.681
## SAT 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.357 0.579
## RI 0.249 0.258 0.381 0.270 0.282 0.373 0.265 0.230 0.000 0.000
## COI 0.023 -0.033 0.212 0.052 0.032 -0.053 0.056 0.002 0.000 0.000
## RI COI
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI 1.000
## COI 0.081 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN .
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN .
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI COI
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI .
## COI NaN .
arrange(modificationindices(SEM_fit),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 AFCOM =~ C_REP1 61.877 0.158 0.177 0.240 0.240
## 2 ATMOS ~~ AFCOM 49.054 -0.587 -0.507 -0.507 -0.507
## 3 ATMOS ~ AFCOM 35.588 -0.540 -0.483 -0.483 -0.483
## 4 AFCOM ~~ RI 32.373 0.134 0.247 0.247 0.247
## 5 COM_A1 ~~ COM_A2 31.301 0.288 0.288 0.368 0.368
## 6 AFCOM ~~ COI 31.255 0.406 0.268 0.268 0.268
## 7 ATMOS =~ C_REP1 26.283 0.102 0.127 0.173 0.173
## 8 Im16 ~~ Im19 25.773 0.371 0.371 0.761 0.761
## 9 PROF ~~ SAT 25.773 -0.222 -0.368 -0.368 -0.368
## 10 BRAND =~ Im13 23.807 0.219 0.264 0.219 0.219
## 11 C_REP2 ~~ C_REP3 23.244 0.096 0.096 1.407 1.407
## 12 SAT ~~ RI 22.140 0.089 0.229 0.229 0.229
## 13 Im11 ~~ Im13 21.621 -0.192 -0.192 -0.341 -0.341
## 14 SAT =~ C_REP1 18.223 0.115 0.099 0.135 0.135
## 15 RI =~ SAT_2 17.895 0.232 0.137 0.137 0.137
## 16 BRAND =~ Im12 17.152 -0.178 -0.214 -0.189 -0.189
## 17 CHOICE =~ Im20 16.326 -0.160 -0.208 -0.139 -0.139
## 18 RI =~ Im22 15.906 -0.338 -0.199 -0.130 -0.130
## 19 RI =~ COM_A1 15.392 0.299 0.176 0.123 0.123
## 20 PROF ~ SAT 14.568 -0.337 -0.322 -0.322 -0.322
## 21 CHOICE =~ Im13 14.137 0.134 0.175 0.145 0.145
## 22 Im11 ~~ Im12 13.137 0.144 0.144 0.286 0.286
## 23 COM_A3 ~~ C_REP1 13.055 0.078 0.078 0.188 0.188
## 24 FOOD =~ Im11 12.685 0.215 0.174 0.152 0.152
## 25 AFCOM =~ Im11 11.893 0.138 0.154 0.135 0.135
## 26 CHOICE =~ C_REP1 11.775 0.059 0.077 0.104 0.104
## 27 SAT ~ FRENCH 11.592 0.143 0.163 0.163 0.163
## 28 PRODQUAL =~ C_CR4 11.365 0.307 0.216 0.109 0.109
## 29 PROF =~ COM_A3 11.354 0.198 0.180 0.112 0.112
## 30 Im21 ~~ C_REP3 11.319 0.052 0.052 0.171 0.171
## 31 ATMOS =~ Im12 11.112 -0.116 -0.146 -0.128 -0.128
## 32 AFCOM =~ Im20 10.705 -0.168 -0.188 -0.126 -0.126
## 33 FRENCH =~ C_REP1 10.658 0.075 0.074 0.100 0.100
## 34 CHOICE =~ Im12 10.534 -0.111 -0.144 -0.127 -0.127
## 35 Im21 ~~ Im22 10.334 -0.190 -0.190 -0.299 -0.299
## 36 Im13 ~~ Im1 10.251 0.066 0.066 0.382 0.382
## 37 PRODQUAL ~~ AFCOM 9.881 -0.142 -0.219 -0.219 -0.219
## 38 DECO =~ C_REP1 9.764 0.056 0.069 0.094 0.094
## 39 AFCOM ~ CHOICE 9.453 0.130 0.151 0.151 0.151
## 40 SAT =~ COM_A2 9.449 -0.194 -0.168 -0.106 -0.106
## 41 Im13 ~~ Im17 9.292 0.068 0.068 0.358 0.358
## 42 SAT =~ COM_A3 9.262 0.199 0.173 0.107 0.107
## 43 AFCOM ~ SAT 9.120 0.359 0.278 0.278 0.278
## 44 Im4 ~~ Im17 9.042 -0.045 -0.045 -0.453 -0.453
## 45 Im1 ~~ SAT_2 9.041 -0.055 -0.055 -0.346 -0.346
## 46 PRODQUAL ~ AFCOM 8.849 -0.148 -0.235 -0.235 -0.235
## 47 SAT ~ AFCOM 8.555 0.220 0.284 0.284 0.284
## 48 Im20 ~~ Im22 8.506 0.205 0.205 0.333 0.333
## 49 Im10 ~~ Im16 8.198 0.046 0.046 0.173 0.173
## 50 SAT =~ Im12 8.068 -0.129 -0.112 -0.099 -0.099
## 51 ATMOS =~ Im11 7.837 0.111 0.138 0.121 0.121
## 52 AFCOM =~ Im12 7.657 -0.091 -0.102 -0.090 -0.090
## 53 Im14 ~~ Im16 7.416 -0.043 -0.043 -0.212 -0.212
## 54 Im20 ~~ Im21 7.388 0.150 0.150 0.219 0.219
## 55 PRODQUAL =~ C_CR1 7.333 -0.237 -0.166 -0.086 -0.086
## 56 FRENCH =~ Im22 7.319 0.137 0.135 0.088 0.088
## 57 COI =~ C_REP1 7.224 0.036 0.060 0.081 0.081
## 58 ATMOS =~ C_CR4 7.213 0.140 0.176 0.089 0.089
## 59 Im10 ~~ COM_A2 7.207 0.049 0.049 0.162 0.162
## 60 DECO =~ COM_A3 7.153 0.107 0.132 0.082 0.082
## 61 BRAND =~ Im20 7.150 -0.123 -0.148 -0.099 -0.099
## 62 FOOD =~ C_REP1 7.149 0.074 0.060 0.081 0.081
## 63 CHOICE =~ C_REP3 7.114 -0.037 -0.048 -0.086 -0.086
## 64 SAT =~ C_CR4 7.053 0.194 0.169 0.086 0.086
## 65 COM_A1 ~~ COM_A4 7.039 -0.148 -0.148 -0.183 -0.183
## 66 FRENCH =~ C_REP2 7.027 -0.050 -0.050 -0.079 -0.079
## 67 ATMOS =~ C_REP3 6.995 -0.042 -0.053 -0.094 -0.094
## 68 AFCOM ~ PROF 6.907 0.199 0.162 0.162 0.162
## 69 BRAND =~ Im22 6.898 0.122 0.148 0.097 0.097
## 70 SAT ~~ COI 6.822 -0.152 -0.140 -0.140 -0.140
## 71 Im19 ~~ C_REP1 6.618 -0.040 -0.040 -0.145 -0.145
## 72 RI =~ Im16 6.453 -0.207 -0.122 -0.101 -0.101
## 73 Im10 ~~ Im6 6.414 -0.036 -0.036 -0.152 -0.152
## 74 FRENCH =~ Im16 6.315 -0.127 -0.126 -0.104 -0.104
## 75 CHOICE =~ Im5 6.298 0.086 0.112 0.085 0.085
## 76 BRAND =~ Im4 6.287 -0.067 -0.081 -0.060 -0.060
## 77 PROF =~ Im12 6.238 -0.152 -0.138 -0.122 -0.122
## 78 PRODQUAL =~ Im5 6.228 0.173 0.121 0.091 0.091
## 79 BRAND =~ C_CR4 6.197 0.127 0.153 0.078 0.078
## 80 PROF =~ C_REP1 6.135 0.069 0.062 0.085 0.085
## 81 Im22 ~~ Im1 6.117 0.062 0.062 0.296 0.296
## 82 ATMOS =~ Im5 6.069 0.095 0.119 0.089 0.089
## 83 C_REP1 ~~ C_REP2 6.068 -0.076 -0.076 -0.909 -0.909
## 84 SAT_2 ~~ SAT_3 6.011 -0.090 -0.090 -0.177 -0.177
## 85 DECO =~ C_CR4 5.821 0.119 0.147 0.075 0.075
## 86 BRAND =~ Im5 5.807 0.096 0.115 0.087 0.087
## 87 FOOD =~ Im6 5.787 -0.269 -0.218 -0.182 -0.182
## 88 BRAND =~ COM_A3 5.704 0.099 0.120 0.074 0.074
## 89 PROF =~ C_CR4 5.642 0.168 0.153 0.078 0.078
## 90 Im13 ~~ Im16 5.612 -0.070 -0.070 -0.144 -0.144
## 91 DECO =~ Im18 5.593 0.101 0.125 0.089 0.089
## 92 DECO =~ Im17 5.593 -0.102 -0.126 -0.101 -0.101
## 93 SAT_1 ~~ SAT_3 5.570 0.092 0.092 0.200 0.200
## 94 COM_A3 ~~ COM_A4 5.532 0.152 0.152 0.176 0.176
## 95 Im3 ~~ Im1 5.490 -0.034 -0.034 -0.265 -0.265
## 96 Im10 ~~ Im7 5.466 0.034 0.034 0.252 0.252
## 97 COM_A1 ~~ C_REP2 5.455 0.034 0.034 0.207 0.207
## 98 Im22 ~~ Im12 5.408 -0.068 -0.068 -0.163 -0.163
## 99 Im11 ~~ Im6 5.400 -0.072 -0.072 -0.116 -0.116
## 100 AFCOM =~ C_CR4 5.370 0.129 0.144 0.073 0.073
## 101 Im22 ~~ C_REP2 5.355 -0.033 -0.033 -0.234 -0.234
## 102 Im16 ~~ SAT_1 5.322 -0.061 -0.061 -0.150 -0.150
## 103 ATMOS =~ C_REP2 5.286 -0.039 -0.049 -0.077 -0.077
## 104 FOOD =~ COM_A3 5.281 0.140 0.113 0.070 0.070
## 105 Im1 ~~ SAT_1 5.167 0.041 0.041 0.287 0.287
## 106 DECO =~ Im20 5.076 -0.095 -0.117 -0.079 -0.079
## 107 DECO =~ C_REP3 5.036 -0.032 -0.040 -0.072 -0.072
## 108 FOOD =~ Im13 5.010 -0.125 -0.102 -0.084 -0.084
## 109 Im5 ~~ Im6 5.010 -0.066 -0.066 -0.112 -0.112
## 110 DECO =~ C_CR1 5.008 -0.106 -0.131 -0.068 -0.068
## 111 DECO =~ Im7 4.885 -0.084 -0.104 -0.086 -0.086
## 112 PROF =~ COM_A2 4.882 -0.125 -0.114 -0.071 -0.071
## 113 CHOICE ~~ AFCOM 4.865 0.101 0.084 0.084 0.084
## 114 C_REP1 ~~ C_REP3 4.856 -0.036 -0.036 -0.225 -0.225
## 115 Im4 ~~ C_CR1 4.822 -0.064 -0.064 -0.191 -0.191
## 116 Im4 ~~ Im18 4.818 0.040 0.040 0.168 0.168
## 117 Im10 ~~ Im13 4.805 -0.031 -0.031 -0.145 -0.145
## 118 FOOD =~ C_REP2 4.798 -0.051 -0.041 -0.065 -0.065
## 119 Im13 ~~ Im2 4.787 -0.045 -0.045 -0.129 -0.129
## 120 Im3 ~~ Im22 4.764 0.049 0.049 0.139 0.139
## 121 FRENCH =~ Im20 4.724 -0.109 -0.107 -0.072 -0.072
## 122 FOOD =~ Im5 4.677 0.120 0.097 0.073 0.073
## 123 FOOD =~ Im7 4.663 0.284 0.230 0.190 0.190
## 124 Im22 ~~ C_REP3 4.654 -0.034 -0.034 -0.123 -0.123
## 125 Im20 ~~ Im17 4.627 -0.058 -0.058 -0.233 -0.233
## 126 PROF =~ SAT_2 4.584 0.130 0.118 0.119 0.119
## 127 Im22 ~~ SAT_1 4.558 0.058 0.058 0.148 0.148
## 128 PROF =~ C_REP3 4.558 -0.048 -0.043 -0.078 -0.078
## 129 Im4 ~~ COM_A3 4.540 0.051 0.051 0.168 0.168
## 130 BRAND =~ C_CR1 4.516 -0.104 -0.126 -0.065 -0.065
## 131 CHOICE ~ AFCOM 4.498 0.114 0.098 0.098 0.098
## 132 Im11 ~~ C_REP1 4.467 0.041 0.041 0.102 0.102
## 133 COM_A1 ~~ SAT_1 4.359 -0.059 -0.059 -0.128 -0.128
## 134 COI =~ COM_A4 4.335 0.063 0.104 0.060 0.060
## 135 Im3 ~~ Im4 4.333 0.148 0.148 0.977 0.977
## 136 RI =~ Im12 4.281 -0.133 -0.078 -0.069 -0.069
## 137 Im3 ~~ Im5 4.266 -0.068 -0.068 -0.169 -0.169
## 138 FRENCH ~~ SAT 4.214 0.060 0.093 0.093 0.093
## 139 COI =~ SAT_1 4.213 -0.039 -0.064 -0.063 -0.063
## 140 BRAND =~ Im7 4.204 -0.079 -0.096 -0.079 -0.079
## 141 AFCOM =~ Im5 4.180 0.079 0.088 0.066 0.066
## 142 DECO =~ Im6 4.175 0.067 0.083 0.069 0.069
## 143 RI =~ Im21 4.151 0.163 0.096 0.070 0.070
## 144 ATMOS =~ Im4 4.122 -0.052 -0.065 -0.048 -0.048
## 145 Im14 ~~ COM_A2 4.095 -0.036 -0.036 -0.156 -0.156
## 146 PRODQUAL =~ Im2 4.068 -0.124 -0.087 -0.068 -0.068
## 147 DECO =~ COM_A2 4.009 -0.077 -0.095 -0.059 -0.059
## 148 Im20 ~~ Im6 3.960 -0.062 -0.062 -0.111 -0.111
## 149 CHOICE =~ COM_A3 3.948 0.074 0.097 0.060 0.060
## 150 PROF =~ Im13 3.914 0.126 0.114 0.095 0.095
## 151 SAT =~ C_CR1 3.891 -0.138 -0.120 -0.062 -0.062
## 152 PROF =~ Im20 3.844 -0.126 -0.115 -0.077 -0.077
## 153 BRAND =~ C_REP3 3.843 -0.029 -0.036 -0.064 -0.064
## 154 Im16 ~~ C_REP3 3.839 -0.029 -0.029 -0.102 -0.102
## 155 BRAND =~ Im6 3.805 0.065 0.079 0.066 0.066
## 156 PRODQUAL =~ Im1 3.759 0.134 0.094 0.071 0.071
## 157 Im7 ~~ C_REP2 3.754 -0.022 -0.022 -0.298 -0.298
## 158 DECO =~ Im22 3.749 0.083 0.102 0.067 0.067
## 159 COM_A4 ~~ C_CR4 3.747 0.121 0.121 0.112 0.112
## 160 FOOD =~ C_CR4 3.740 0.147 0.119 0.060 0.060
## 161 SAT ~ ATMOS 3.739 0.072 0.104 0.104 0.104
## 162 SAT_3 ~~ C_CR3 3.717 -0.111 -0.111 -0.106 -0.106
## 163 COI =~ Im19 3.711 0.050 0.083 0.073 0.073
## 164 COM_A2 ~~ SAT_2 3.687 -0.057 -0.057 -0.113 -0.113
## 165 Im20 ~~ COM_A4 3.684 0.085 0.085 0.113 0.113
## 166 Im20 ~~ Im13 3.683 0.061 0.061 0.120 0.120
## 167 Im4 ~~ Im6 3.674 0.033 0.033 0.148 0.148
## 168 Im11 ~~ Im1 3.661 -0.047 -0.047 -0.190 -0.190
## 169 Im22 ~~ SAT_2 3.643 -0.053 -0.053 -0.121 -0.121
## 170 RI =~ Im5 3.628 0.136 0.080 0.060 0.060
## 171 COM_A1 ~~ COM_A3 3.553 -0.099 -0.099 -0.120 -0.120
## 172 COM_A2 ~~ COM_A3 3.545 -0.111 -0.111 -0.134 -0.134
## 173 SAT_1 ~~ C_CR1 3.534 -0.069 -0.069 -0.130 -0.130
## 174 Im3 ~~ COM_A4 3.528 0.048 0.048 0.112 0.112
## 175 Im22 ~~ Im11 3.500 0.071 0.071 0.105 0.105
## 176 PROF =~ C_CR1 3.432 -0.126 -0.115 -0.059 -0.059
## 177 Im2 ~~ Im17 3.429 0.032 0.032 0.188 0.188
## 178 ATMOS =~ COM_A4 3.391 0.094 0.118 0.069 0.069
## 179 Im3 ~~ Im17 3.378 0.028 0.028 0.201 0.201
## 180 Im13 ~~ C_REP2 3.372 0.022 0.022 0.185 0.185
## 181 Im22 ~~ C_REP1 3.355 0.035 0.035 0.105 0.105
## 182 PROF =~ Im2 3.355 0.161 0.147 0.114 0.114
## 183 PROF =~ Im1 3.354 -0.181 -0.165 -0.124 -0.124
## 184 C_REP2 ~~ C_CR4 3.348 -0.037 -0.037 -0.171 -0.171
## 185 FRENCH ~ SAT 3.327 0.124 0.109 0.109 0.109
## 186 Im13 ~~ C_REP1 3.251 -0.029 -0.029 -0.103 -0.103
## 187 Im20 ~~ SAT_2 3.249 0.050 0.050 0.108 0.108
## 188 Im14 ~~ Im6 3.218 0.025 0.025 0.142 0.142
## 189 COI =~ C_REP2 3.212 -0.020 -0.033 -0.052 -0.052
## 190 Im22 ~~ COM_A1 3.204 -0.071 -0.071 -0.106 -0.106
## 191 AFCOM =~ C_REP3 3.175 -0.029 -0.033 -0.058 -0.058
## 192 COI =~ Im11 3.174 0.048 0.078 0.069 0.069
## 193 PROF =~ SAT_1 3.159 -0.113 -0.103 -0.102 -0.102
## 194 Im1 ~~ C_REP3 3.154 -0.018 -0.018 -0.179 -0.179
## 195 Im11 ~~ Im17 3.129 -0.047 -0.047 -0.169 -0.169
## 196 COM_A2 ~~ C_CR1 3.120 0.099 0.099 0.108 0.108
## 197 Im20 ~~ COM_A2 3.119 -0.074 -0.074 -0.102 -0.102
## 198 Im18 ~~ Im6 3.098 0.046 0.046 0.092 0.092
## 199 Im17 ~~ C_REP1 3.076 -0.023 -0.023 -0.172 -0.172
## 200 Im5 ~~ C_REP1 3.034 0.032 0.032 0.084 0.084
## 201 FRENCH =~ Im11 3.032 0.081 0.080 0.070 0.070
## 202 PRODQUAL =~ Im16 3.000 -0.148 -0.104 -0.087 -0.087
## 203 Im14 ~~ SAT_2 2.981 0.021 0.021 0.139 0.139
## 204 PRODQUAL =~ C_REP3 2.970 -0.046 -0.033 -0.059 -0.059
## 205 Im18 ~~ COM_A1 2.961 -0.057 -0.057 -0.090 -0.090
## 206 Im3 ~~ Im2 2.955 0.025 0.025 0.097 0.097
## 207 BRAND =~ C_REP1 2.929 0.032 0.038 0.052 0.052
## 208 COM_A1 ~~ C_CR3 2.928 0.099 0.099 0.096 0.096
## 209 Im13 ~~ COM_A2 2.909 -0.058 -0.058 -0.104 -0.104
## 210 Im14 ~~ Im7 2.900 -0.025 -0.025 -0.243 -0.243
## 211 COM_A4 ~~ SAT_1 2.891 0.053 0.053 0.111 0.111
## 212 FRENCH =~ C_CR4 2.880 0.108 0.106 0.054 0.054
## 213 Im5 ~~ Im1 2.857 0.040 0.040 0.168 0.168
## 214 FRENCH =~ COM_A3 2.841 0.090 0.089 0.055 0.055
## 215 ATMOS =~ COM_A1 2.817 -0.076 -0.095 -0.067 -0.067
## 216 Im10 ~~ Im11 2.794 0.028 0.028 0.092 0.092
## 217 Im22 ~~ Im2 2.792 -0.042 -0.042 -0.099 -0.099
## 218 SAT =~ Im19 2.751 -0.121 -0.105 -0.093 -0.093
## 219 Im10 ~~ C_CR1 2.731 0.038 0.038 0.109 0.109
## 220 Im14 ~~ C_CR1 2.727 -0.037 -0.037 -0.140 -0.140
## 221 SAT_2 ~~ C_REP1 2.724 0.023 0.023 0.090 0.090
## 222 Im5 ~~ Im14 2.721 0.026 0.026 0.117 0.117
## 223 Im2 ~~ C_CR1 2.710 0.056 0.056 0.098 0.098
## 224 RI =~ Im11 2.694 0.124 0.073 0.064 0.064
## 225 Im5 ~~ Im7 2.692 0.047 0.047 0.137 0.137
## 226 COM_A1 ~~ SAT_3 2.689 0.066 0.066 0.084 0.084
## 227 SAT =~ Im5 2.676 0.086 0.074 0.056 0.056
## 228 Im21 ~~ C_CR3 2.672 -0.091 -0.091 -0.092 -0.092
## 229 Im2 ~~ SAT_2 2.671 0.030 0.030 0.093 0.093
## 230 Im1 ~~ Im17 2.669 -0.029 -0.029 -0.347 -0.347
## 231 Im12 ~~ Im7 2.643 0.038 0.038 0.172 0.172
## 232 SAT =~ Im20 2.596 -0.092 -0.080 -0.053 -0.053
## 233 Im19 ~~ SAT_1 2.588 -0.038 -0.038 -0.117 -0.117
## 234 Im2 ~~ Im16 2.587 0.038 0.038 0.087 0.087
## 235 COM_A2 ~~ SAT_1 2.580 -0.047 -0.047 -0.103 -0.103
## 236 Im20 ~~ COM_A1 2.563 -0.064 -0.064 -0.089 -0.089
## 237 CHOICE =~ Im22 2.551 0.064 0.083 0.054 0.054
## 238 ATMOS =~ C_CR1 2.545 -0.080 -0.100 -0.052 -0.052
## 239 ATMOS =~ Im13 2.531 0.058 0.073 0.061 0.061
## 240 C_REP3 ~~ C_CR3 2.505 -0.037 -0.037 -0.086 -0.086
## 241 Im14 ~~ C_REP3 2.490 0.011 0.011 0.114 0.114
## 242 AFCOM =~ SAT_2 2.425 0.053 0.060 0.060 0.060
## 243 Im2 ~~ C_REP1 2.403 0.020 0.020 0.079 0.079
## 244 Im4 ~~ Im11 2.402 -0.033 -0.033 -0.112 -0.112
## 245 Im3 ~~ C_CR1 2.396 0.047 0.047 0.099 0.099
## 246 Im4 ~~ Im22 2.381 -0.033 -0.033 -0.134 -0.134
## 247 COM_A4 ~~ SAT_3 2.375 -0.069 -0.069 -0.083 -0.083
## 248 CHOICE =~ Im14 2.365 0.026 0.034 0.039 0.039
## 249 CHOICE =~ Im10 2.364 -0.025 -0.033 -0.038 -0.038
## 250 Im5 ~~ COM_A2 2.363 0.061 0.061 0.079 0.079
## 251 FOOD =~ C_CR1 2.363 -0.112 -0.091 -0.047 -0.047
## 252 Im22 ~~ SAT_3 2.338 -0.060 -0.060 -0.088 -0.088
## 253 Im11 ~~ C_REP2 2.334 -0.022 -0.022 -0.128 -0.128
## 254 SAT =~ Im11 2.319 0.084 0.073 0.064 0.064
## 255 FOOD =~ SAT_2 2.311 0.063 0.051 0.052 0.052
## 256 Im20 ~~ Im1 2.293 -0.038 -0.038 -0.169 -0.169
## 257 COM_A4 ~~ C_REP1 2.283 0.033 0.033 0.081 0.081
## 258 PRODQUAL =~ SAT_2 2.262 0.078 0.055 0.055 0.055
## 259 COM_A3 ~~ C_REP2 2.256 -0.024 -0.024 -0.136 -0.136
## 260 COM_A2 ~~ COM_A4 2.244 -0.096 -0.096 -0.118 -0.118
## 261 SAT =~ Im16 2.223 -0.113 -0.098 -0.081 -0.081
## 262 FRENCH =~ Im1 2.216 -0.051 -0.050 -0.038 -0.038
## 263 FOOD =~ Im16 2.214 -0.100 -0.081 -0.067 -0.067
## 264 Im21 ~~ Im18 2.214 -0.047 -0.047 -0.078 -0.078
## 265 Im13 ~~ COM_A3 2.212 -0.052 -0.052 -0.090 -0.090
## 266 SAT =~ Im13 2.196 0.072 0.062 0.052 0.052
## 267 Im2 ~~ C_REP2 2.177 -0.014 -0.014 -0.131 -0.131
## 268 Im22 ~~ Im7 2.176 0.044 0.044 0.149 0.149
## 269 Im19 ~~ COM_A1 2.173 0.047 0.047 0.086 0.086
## 270 AFCOM =~ Im2 2.170 0.041 0.045 0.035 0.035
## 271 COM_A3 ~~ C_REP3 2.156 -0.026 -0.026 -0.076 -0.076
## 272 DECO =~ Im12 2.149 -0.052 -0.065 -0.057 -0.057
## 273 Im5 ~~ Im16 2.143 -0.051 -0.051 -0.074 -0.074
## 274 Im13 ~~ SAT_2 2.137 0.033 0.033 0.092 0.092
## 275 FRENCH =~ SAT_1 2.131 0.048 0.048 0.047 0.047
## 276 Im3 ~~ Im20 2.127 -0.033 -0.033 -0.087 -0.087
## 277 COI =~ Im2 2.123 0.025 0.042 0.032 0.032
## 278 Im4 ~~ Im1 2.121 0.020 0.020 0.226 0.226
## 279 COI =~ Im13 2.103 -0.034 -0.056 -0.046 -0.046
## 280 COI =~ COM_A2 2.066 0.041 0.068 0.043 0.043
## 281 Im3 ~~ COM_A3 2.063 -0.036 -0.036 -0.084 -0.084
## 282 BRAND =~ SAT_2 2.060 0.043 0.052 0.052 0.052
## 283 PRODQUAL =~ Im6 2.054 -0.086 -0.060 -0.050 -0.050
## 284 PRODQUAL =~ Im7 2.054 0.100 0.070 0.058 0.058
## 285 Im22 ~~ Im19 2.047 -0.045 -0.045 -0.095 -0.095
## 286 Im10 ~~ Im17 2.044 -0.017 -0.017 -0.162 -0.162
## 287 Im16 ~~ C_CR4 2.028 -0.074 -0.074 -0.080 -0.080
## 288 Im22 ~~ Im18 2.023 0.046 0.046 0.084 0.084
## 289 FRENCH =~ COM_A2 2.019 -0.073 -0.072 -0.045 -0.045
## 290 Im3 ~~ Im12 2.015 -0.024 -0.024 -0.094 -0.094
## 291 Im12 ~~ Im16 2.003 0.039 0.039 0.090 0.090
## 292 Im2 ~~ SAT_1 1.991 -0.025 -0.025 -0.087 -0.087
## 293 Im12 ~~ SAT_3 1.984 0.042 0.042 0.085 0.085
## 294 Im18 ~~ C_REP1 1.983 0.023 0.023 0.071 0.071
## 295 Im19 ~~ C_REP2 1.960 0.017 0.017 0.143 0.143
## 296 Im21 ~~ C_CR4 1.960 0.076 0.076 0.077 0.077
## 297 Im14 ~~ Im17 1.948 0.016 0.016 0.206 0.206
## 298 Im2 ~~ COM_A3 1.923 0.039 0.039 0.075 0.075
## 299 SAT =~ Im18 1.917 -0.073 -0.064 -0.046 -0.046
## 300 Im14 ~~ COM_A3 1.909 0.026 0.026 0.106 0.106
## 301 Im14 ~~ Im2 1.900 0.015 0.015 0.103 0.103
## 302 FOOD =~ Im1 1.888 -0.060 -0.049 -0.037 -0.037
## 303 Im12 ~~ SAT_1 1.877 -0.028 -0.028 -0.098 -0.098
## 304 C_CR1 ~~ C_CR3 1.851 0.543 0.543 0.451 0.451
## 305 Im10 ~~ COM_A4 1.834 -0.026 -0.026 -0.083 -0.083
## 306 Im7 ~~ COM_A1 1.820 -0.041 -0.041 -0.119 -0.119
## 307 Im11 ~~ Im7 1.810 0.040 0.040 0.112 0.112
## 308 Im11 ~~ COM_A3 1.799 0.058 0.058 0.068 0.068
## 309 COM_A3 ~~ SAT_2 1.794 0.042 0.042 0.078 0.078
## 310 SAT =~ Im2 1.787 0.065 0.056 0.044 0.044
## 311 BRAND =~ Im3 1.782 0.035 0.042 0.032 0.032
## 312 Im20 ~~ SAT_1 1.779 -0.036 -0.036 -0.086 -0.086
## 313 COM_A2 ~~ SAT_3 1.771 0.056 0.056 0.071 0.071
## 314 COM_A1 ~~ C_REP3 1.769 0.022 0.022 0.067 0.067
## 315 CHOICE =~ SAT_2 1.768 -0.041 -0.054 -0.054 -0.054
## 316 CHOICE =~ C_CR4 1.742 0.062 0.080 0.041 0.041
## 317 ATMOS =~ SAT_2 1.740 0.037 0.047 0.047 0.047
## 318 PROF =~ Im4 1.737 -0.065 -0.059 -0.044 -0.044
## 319 Im10 ~~ SAT_2 1.735 -0.016 -0.016 -0.083 -0.083
## 320 FRENCH =~ Im5 1.729 0.059 0.058 0.043 0.043
## 321 Im19 ~~ Im17 1.718 0.030 0.030 0.158 0.158
## 322 FRENCH =~ C_CR1 1.715 -0.080 -0.079 -0.041 -0.041
## 323 Im20 ~~ COM_A3 1.713 -0.057 -0.057 -0.075 -0.075
## 324 Im7 ~~ COM_A2 1.692 -0.042 -0.042 -0.119 -0.119
## 325 COI =~ Im1 1.689 -0.025 -0.042 -0.031 -0.031
## 326 Im12 ~~ Im6 1.663 -0.030 -0.030 -0.080 -0.080
## 327 RI =~ Im14 1.662 0.047 0.028 0.032 0.032
## 328 RI =~ Im10 1.662 -0.046 -0.027 -0.031 -0.031
## 329 Im13 ~~ COM_A4 1.659 0.046 0.046 0.080 0.080
## 330 RI =~ Im7 1.647 -0.094 -0.055 -0.046 -0.046
## 331 Im11 ~~ Im2 1.627 0.032 0.032 0.063 0.063
## 332 COI =~ Im22 1.622 -0.037 -0.061 -0.040 -0.040
## 333 Im3 ~~ Im14 1.617 -0.012 -0.012 -0.103 -0.103
## 334 C_REP1 ~~ C_CR3 1.612 0.036 0.036 0.069 0.069
## 335 Im5 ~~ SAT_2 1.610 0.034 0.034 0.068 0.068
## 336 PRODQUAL =~ Im4 1.608 -0.058 -0.041 -0.030 -0.030
## 337 RI =~ Im19 1.585 -0.099 -0.058 -0.052 -0.052
## 338 Im12 ~~ C_CR4 1.580 0.053 0.053 0.081 0.081
## 339 COI =~ Im4 1.558 -0.020 -0.032 -0.024 -0.024
## 340 SAT =~ Im17 1.554 0.057 0.049 0.040 0.040
## 341 Im7 ~~ SAT_3 1.540 0.038 0.038 0.107 0.107
## 342 Im12 ~~ Im17 1.539 -0.026 -0.026 -0.154 -0.154
## 343 Im17 ~~ COM_A1 1.518 0.033 0.033 0.124 0.124
## 344 FRENCH =~ Im2 1.509 0.038 0.037 0.029 0.029
## 345 Im1 ~~ COM_A4 1.504 -0.034 -0.034 -0.135 -0.135
## 346 Im10 ~~ Im18 1.499 0.018 0.018 0.071 0.071
## 347 Im4 ~~ Im2 1.495 -0.017 -0.017 -0.094 -0.094
## 348 RI =~ Im13 1.495 0.082 0.048 0.040 0.040
## 349 CHOICE =~ Im21 1.486 0.046 0.060 0.043 0.043
## 350 Im2 ~~ Im18 1.484 -0.026 -0.026 -0.063 -0.063
## 351 CHOICE ~ SAT 1.479 0.210 0.140 0.140 0.140
## 352 C_REP3 ~~ C_CR4 1.479 0.027 0.027 0.064 0.064
## 353 Im11 ~~ SAT_1 1.457 0.033 0.033 0.070 0.070
## 354 PROF =~ Im5 1.424 0.081 0.074 0.055 0.055
## 355 DECO =~ Im13 1.423 0.045 0.055 0.046 0.046
## 356 Im12 ~~ Im13 1.421 0.088 0.088 0.252 0.252
## 357 Im18 ~~ COM_A2 1.416 0.041 0.041 0.064 0.064
## 358 COM_A1 ~~ SAT_2 1.415 0.034 0.034 0.067 0.067
## 359 FOOD =~ Im2 1.413 0.046 0.038 0.029 0.029
## 360 Im12 ~~ C_REP1 1.409 -0.018 -0.018 -0.071 -0.071
## 361 AFCOM ~ DECO 1.398 0.054 0.059 0.059 0.059
## 362 DECO ~~ SAT 1.396 -0.146 -0.179 -0.179 -0.179
## 363 Im14 ~~ Im18 1.395 -0.016 -0.016 -0.088 -0.088
## 364 Im21 ~~ SAT_3 1.392 0.045 0.045 0.061 0.061
## 365 SAT =~ COM_A1 1.385 0.070 0.061 0.043 0.043
## 366 Im1 ~~ COM_A1 1.385 0.030 0.030 0.123 0.123
## 367 Im18 ~~ Im7 1.381 -0.029 -0.029 -0.103 -0.103
## 368 COM_A3 ~~ C_CR3 1.376 0.074 0.074 0.068 0.068
## 369 SAT_2 ~~ C_CR3 1.376 0.048 0.048 0.071 0.071
## 370 Im14 ~~ C_CR4 1.375 0.028 0.028 0.092 0.092
## 371 Im10 ~~ Im12 1.375 0.015 0.015 0.081 0.081
## 372 SAT =~ Im4 1.372 -0.039 -0.034 -0.025 -0.025
## 373 AFCOM =~ Im16 1.367 -0.047 -0.053 -0.044 -0.044
## 374 Im3 ~~ Im18 1.357 -0.022 -0.022 -0.066 -0.066
## 375 Im19 ~~ Im18 1.354 -0.031 -0.031 -0.068 -0.068
## 376 Im18 ~~ C_REP3 1.351 -0.015 -0.015 -0.058 -0.058
## 377 ATMOS =~ Im17 1.348 -0.052 -0.065 -0.053 -0.053
## 378 ATMOS =~ Im18 1.348 0.052 0.065 0.046 0.046
## 379 Im4 ~~ Im12 1.347 0.019 0.019 0.105 0.105
## 380 CHOICE =~ COM_A1 1.346 0.040 0.052 0.036 0.036
## 381 Im5 ~~ Im19 1.341 -0.034 -0.034 -0.064 -0.064
## 382 Im13 ~~ SAT_3 1.338 -0.037 -0.037 -0.066 -0.066
## 383 Im3 ~~ Im11 1.307 0.026 0.026 0.061 0.061
## 384 SAT_1 ~~ C_CR4 1.304 0.044 0.044 0.073 0.073
## 385 ATMOS =~ COM_A2 1.298 -0.055 -0.069 -0.043 -0.043
## 386 Im20 ~~ C_REP2 1.295 0.016 0.016 0.108 0.108
## 387 BRAND =~ Im16 1.284 -0.059 -0.071 -0.059 -0.059
## 388 SAT_1 ~~ C_REP3 1.284 0.013 0.013 0.067 0.067
## 389 Im6 ~~ Im7 1.281 0.435 0.435 1.612 1.612
## 390 FRENCH ~~ AFCOM 1.280 -0.077 -0.085 -0.085 -0.085
## 391 RI =~ COM_A3 1.276 0.094 0.055 0.034 0.034
## 392 PRODQUAL =~ Im17 1.271 0.103 0.072 0.058 0.058
## 393 PRODQUAL =~ Im18 1.271 -0.102 -0.072 -0.051 -0.051
## 394 Im14 ~~ Im21 1.262 0.018 0.018 0.084 0.084
## 395 Im22 ~~ C_CR1 1.256 -0.058 -0.058 -0.075 -0.075
## 396 Im12 ~~ COM_A4 1.239 -0.037 -0.037 -0.072 -0.072
## 397 RI =~ COM_A4 1.230 0.093 0.055 0.032 0.032
## 398 Im20 ~~ C_REP3 1.225 -0.018 -0.018 -0.059 -0.059
## 399 Im3 ~~ Im10 1.223 0.011 0.011 0.070 0.070
## 400 PRODQUAL =~ COM_A2 1.213 -0.078 -0.055 -0.035 -0.035
## 401 FRENCH =~ SAT_3 1.209 0.051 0.050 0.044 0.044
## 402 Im10 ~~ C_CR4 1.207 -0.027 -0.027 -0.067 -0.067
## 403 Im4 ~~ COM_A4 1.202 -0.027 -0.027 -0.089 -0.089
## 404 PRODQUAL =~ Im20 1.186 0.083 0.058 0.039 0.039
## 405 PROF ~~ AFCOM 1.182 0.034 0.040 0.040 0.040
## 406 CHOICE =~ SAT_1 1.178 0.035 0.046 0.045 0.045
## 407 COI =~ Im20 1.152 -0.031 -0.051 -0.034 -0.034
## 408 PRODQUAL =~ Im22 1.149 -0.083 -0.058 -0.038 -0.038
## 409 Im10 ~~ C_REP3 1.147 -0.007 -0.007 -0.060 -0.060
## 410 SAT_1 ~~ C_CR3 1.144 -0.042 -0.042 -0.070 -0.070
## 411 COI =~ SAT_2 1.136 0.020 0.034 0.034 0.034
## 412 Im16 ~~ Im7 1.135 -0.030 -0.030 -0.098 -0.098
## 413 PRODQUAL =~ Im19 1.134 0.088 0.062 0.055 0.055
## 414 Im1 ~~ COM_A3 1.105 -0.029 -0.029 -0.113 -0.113
## 415 Im16 ~~ C_CR1 1.098 0.052 0.052 0.064 0.064
## 416 Im4 ~~ Im7 1.087 -0.018 -0.018 -0.137 -0.137
## 417 Im17 ~~ COM_A3 1.087 0.031 0.031 0.108 0.108
## 418 PROF =~ Im7 1.079 -0.065 -0.059 -0.049 -0.049
## 419 BRAND =~ Im11 1.044 -0.046 -0.055 -0.048 -0.048
## 420 PROF =~ COM_A1 1.028 0.055 0.050 0.035 0.035
## 421 Im1 ~~ COM_A2 1.000 0.027 0.027 0.108 0.108
## 422 Im6 ~~ SAT_1 0.995 0.022 0.022 0.062 0.062
## 423 Im13 ~~ C_CR3 0.995 -0.046 -0.046 -0.063 -0.063
## 424 Im14 ~~ Im12 0.989 -0.013 -0.013 -0.089 -0.089
## 425 COM_A4 ~~ C_CR3 0.982 -0.063 -0.063 -0.059 -0.059
## 426 SAT_3 ~~ C_REP3 0.980 0.016 0.016 0.049 0.049
## 427 Im1 ~~ Im18 0.980 0.021 0.021 0.104 0.104
## 428 CHOICE =~ Im16 0.965 0.048 0.063 0.052 0.052
## 429 CHOICE =~ Im19 0.965 -0.050 -0.065 -0.058 -0.058
## 430 ATMOS =~ Im2 0.957 -0.032 -0.040 -0.031 -0.031
## 431 Im16 ~~ COM_A3 0.956 0.040 0.040 0.054 0.054
## 432 Im20 ~~ Im18 0.950 0.032 0.032 0.054 0.054
## 433 Im17 ~~ COM_A4 0.902 -0.028 -0.028 -0.101 -0.101
## 434 Im5 ~~ Im2 0.897 -0.023 -0.023 -0.047 -0.047
## 435 Im13 ~~ Im18 0.892 -0.025 -0.025 -0.056 -0.056
## 436 BRAND =~ SAT_3 0.890 -0.037 -0.045 -0.040 -0.040
## 437 ATMOS =~ Im3 0.886 0.024 0.029 0.022 0.022
## 438 ATMOS =~ C_CR3 0.882 -0.050 -0.063 -0.031 -0.031
## 439 CHOICE ~~ SAT 0.882 -0.110 -0.128 -0.128 -0.128
## 440 Im1 ~~ Im2 0.880 1.034 1.034 6.695 6.695
## 441 SAT =~ Im21 0.870 0.051 0.044 0.032 0.032
## 442 Im11 ~~ COM_A2 0.868 0.038 0.038 0.048 0.048
## 443 FOOD =~ Im20 0.862 -0.054 -0.044 -0.029 -0.029
## 444 Im17 ~~ C_REP3 0.860 0.010 0.010 0.090 0.090
## 445 SAT =~ Im1 0.859 -0.049 -0.043 -0.032 -0.032
## 446 ATMOS ~~ SAT 0.859 0.034 0.041 0.041 0.041
## 447 Im7 ~~ COM_A4 0.857 0.031 0.031 0.087 0.087
## 448 Im11 ~~ C_CR4 0.857 0.051 0.051 0.048 0.048
## 449 DECO =~ C_REP2 0.849 -0.014 -0.017 -0.027 -0.027
## 450 Im6 ~~ C_CR4 0.847 -0.041 -0.041 -0.051 -0.051
## 451 Im3 ~~ SAT_1 0.845 0.015 0.015 0.061 0.061
## 452 DECO =~ SAT_2 0.832 0.026 0.033 0.033 0.033
## 453 Im19 ~~ SAT_3 0.832 -0.029 -0.029 -0.052 -0.052
## 454 Im16 ~~ COM_A4 0.828 -0.037 -0.037 -0.052 -0.052
## 455 Im6 ~~ COM_A1 0.825 0.029 0.029 0.048 0.048
## 456 Im6 ~~ C_REP2 0.824 0.010 0.010 0.081 0.081
## 457 BRAND =~ Im1 0.818 -0.039 -0.047 -0.035 -0.035
## 458 Im4 ~~ C_CR3 0.817 0.029 0.029 0.074 0.074
## 459 Im4 ~~ COM_A2 0.807 -0.021 -0.021 -0.071 -0.071
## 460 COI =~ SAT_3 0.791 -0.024 -0.040 -0.035 -0.035
## 461 Im7 ~~ C_CR4 0.785 0.038 0.038 0.082 0.082
## 462 SAT_2 ~~ C_REP3 0.783 0.010 0.010 0.048 0.048
## 463 BRAND =~ COM_A4 0.778 -0.037 -0.045 -0.026 -0.026
## 464 Im16 ~~ SAT_2 0.778 0.024 0.024 0.052 0.052
## 465 Im20 ~~ Im12 0.776 0.026 0.026 0.058 0.058
## 466 PROF =~ Im18 0.772 -0.078 -0.071 -0.051 -0.051
## 467 PROF =~ Im17 0.772 0.079 0.072 0.058 0.058
## 468 FOOD =~ SAT_3 0.770 0.050 0.040 0.036 0.036
## 469 COI =~ Im5 0.767 0.022 0.037 0.028 0.028
## 470 Im17 ~~ C_REP2 0.767 0.009 0.009 0.155 0.155
## 471 Im7 ~~ C_CR1 0.757 -0.035 -0.035 -0.087 -0.087
## 472 FRENCH =~ COM_A1 0.751 -0.042 -0.042 -0.029 -0.029
## 473 CHOICE =~ C_REP2 0.751 -0.012 -0.016 -0.026 -0.026
## 474 Im14 ~~ SAT_1 0.748 -0.010 -0.010 -0.075 -0.075
## 475 Im21 ~~ Im11 0.737 -0.032 -0.032 -0.043 -0.043
## 476 Im3 ~~ Im19 0.732 0.016 0.016 0.055 0.055
## 477 PROF =~ Im11 0.726 0.054 0.049 0.043 0.043
## 478 BRAND =~ Im2 0.725 0.033 0.039 0.031 0.031
## 479 Im12 ~~ COM_A3 0.724 -0.028 -0.028 -0.054 -0.054
## 480 Im1 ~~ C_REP2 0.720 0.008 0.008 0.154 0.154
## 481 Im14 ~~ Im13 0.716 0.012 0.012 0.072 0.072
## 482 Im20 ~~ Im2 0.715 -0.021 -0.021 -0.047 -0.047
## 483 Im2 ~~ C_REP3 0.715 0.009 0.009 0.043 0.043
## 484 BRAND =~ COM_A2 0.713 -0.034 -0.041 -0.026 -0.026
## 485 Im5 ~~ C_CR3 0.707 -0.045 -0.045 -0.045 -0.045
## 486 Im7 ~~ C_REP3 0.706 0.010 0.010 0.071 0.071
## 487 Im5 ~~ C_CR4 0.704 0.044 0.044 0.044 0.044
## 488 COM_A3 ~~ SAT_3 0.702 -0.037 -0.037 -0.044 -0.044
## 489 Im21 ~~ Im17 0.698 0.022 0.022 0.085 0.085
## 490 Im3 ~~ C_CR4 0.696 -0.027 -0.027 -0.049 -0.049
## 491 Im12 ~~ COM_A2 0.654 0.026 0.026 0.052 0.052
## 492 FOOD =~ COM_A2 0.653 -0.047 -0.038 -0.024 -0.024
## 493 COM_A4 ~~ C_REP3 0.652 -0.014 -0.014 -0.043 -0.043
## 494 PRODQUAL =~ SAT_1 0.651 -0.042 -0.029 -0.029 -0.029
## 495 Im21 ~~ C_REP1 0.650 -0.015 -0.015 -0.041 -0.041
## 496 Im4 ~~ Im5 0.638 0.028 0.028 0.099 0.099
## 497 ATMOS =~ Im1 0.638 0.029 0.036 0.027 0.027
## 498 BRAND =~ Im14 0.638 0.015 0.018 0.021 0.021
## 499 BRAND =~ Im10 0.638 -0.015 -0.018 -0.020 -0.020
## 500 FRENCH =~ Im13 0.638 -0.033 -0.033 -0.027 -0.027
## 501 AFCOM =~ C_REP2 0.636 -0.012 -0.014 -0.022 -0.022
## 502 SAT ~ PRODQUAL 0.629 0.055 0.045 0.045 0.045
## 503 PRODQUAL =~ COM_A3 0.623 0.058 0.041 0.025 0.025
## 504 SAT =~ Im14 0.623 0.020 0.018 0.021 0.021
## 505 PRODQUAL ~ SAT 0.621 -0.038 -0.047 -0.047 -0.047
## 506 ATMOS =~ Im19 0.620 -0.034 -0.043 -0.038 -0.038
## 507 Im4 ~~ Im10 0.613 -0.008 -0.008 -0.067 -0.067
## 508 Im2 ~~ COM_A4 0.612 0.022 0.022 0.043 0.043
## 509 RI =~ Im1 0.609 -0.046 -0.027 -0.020 -0.020
## 510 Im10 ~~ Im2 0.608 -0.009 -0.009 -0.045 -0.045
## 511 Im10 ~~ COM_A3 0.603 -0.015 -0.015 -0.046 -0.046
## 512 ATMOS =~ COM_A3 0.600 0.039 0.048 0.030 0.030
## 513 Im12 ~~ C_CR1 0.600 -0.031 -0.031 -0.054 -0.054
## 514 FOOD ~~ SAT 0.598 0.017 0.032 0.032 0.032
## 515 COM_A2 ~~ C_CR4 0.598 -0.046 -0.046 -0.044 -0.044
## 516 Im22 ~~ Im13 0.597 -0.024 -0.024 -0.051 -0.051
## 517 Im10 ~~ COM_A1 0.593 -0.014 -0.014 -0.045 -0.045
## 518 RI =~ Im4 0.589 -0.034 -0.020 -0.015 -0.015
## 519 Im21 ~~ Im12 0.585 0.022 0.022 0.047 0.047
## 520 Im7 ~~ C_REP1 0.583 0.011 0.011 0.065 0.065
## 521 SAT_3 ~~ C_CR1 0.582 0.041 0.041 0.044 0.044
## 522 Im4 ~~ C_CR4 0.581 0.024 0.024 0.061 0.061
## 523 Im7 ~~ COM_A3 0.566 0.025 0.025 0.068 0.068
## 524 Im20 ~~ Im7 0.551 0.022 0.022 0.070 0.070
## 525 Im14 ~~ Im22 0.549 -0.012 -0.012 -0.063 -0.063
## 526 Im10 ~~ Im21 0.543 -0.012 -0.012 -0.043 -0.043
## 527 Im4 ~~ Im16 0.541 0.015 0.015 0.059 0.059
## 528 PROF =~ Im22 0.532 0.048 0.043 0.028 0.028
## 529 COI =~ Im3 0.531 0.011 0.019 0.014 0.014
## 530 FRENCH =~ Im21 0.520 -0.034 -0.034 -0.025 -0.025
## 531 Im22 ~~ Im6 0.520 0.022 0.022 0.043 0.043
## 532 Im6 ~~ COM_A3 0.519 -0.025 -0.025 -0.039 -0.039
## 533 Im7 ~~ SAT_1 0.513 0.015 0.015 0.074 0.074
## 534 Im22 ~~ Im16 0.512 0.026 0.026 0.043 0.043
## 535 PRODQUAL =~ C_REP2 0.505 0.020 0.014 0.022 0.022
## 536 Im14 ~~ COM_A4 0.504 0.013 0.013 0.056 0.056
## 537 Im11 ~~ Im18 0.501 0.023 0.023 0.035 0.035
## 538 SAT =~ C_CR3 0.500 -0.053 -0.046 -0.022 -0.022
## 539 Im17 ~~ SAT_3 0.500 -0.019 -0.019 -0.070 -0.070
## 540 Im5 ~~ Im11 0.498 0.026 0.026 0.033 0.033
## 541 Im20 ~~ C_CR3 0.491 -0.040 -0.040 -0.042 -0.042
## 542 Im3 ~~ Im7 0.490 -0.012 -0.012 -0.067 -0.067
## 543 Im10 ~~ Im20 0.488 0.012 0.012 0.043 0.043
## 544 CHOICE =~ C_CR1 0.484 -0.031 -0.041 -0.021 -0.021
## 545 Im14 ~~ Im20 0.479 -0.012 -0.012 -0.055 -0.055
## 546 Im12 ~~ Im2 0.478 -0.013 -0.013 -0.043 -0.043
## 547 Im5 ~~ Im10 0.477 -0.011 -0.011 -0.038 -0.038
## 548 Im21 ~~ Im7 0.471 -0.020 -0.020 -0.061 -0.061
## 549 Im1 ~~ C_CR1 0.468 -0.023 -0.023 -0.082 -0.082
## 550 Im10 ~~ SAT_1 0.467 0.008 0.008 0.047 0.047
## 551 Im2 ~~ COM_A1 0.467 -0.018 -0.018 -0.036 -0.036
## 552 PRODQUAL =~ Im14 0.462 0.027 0.019 0.022 0.022
## 553 PRODQUAL =~ Im10 0.462 -0.026 -0.018 -0.021 -0.021
## 554 Im5 ~~ Im21 0.461 -0.025 -0.025 -0.034 -0.034
## 555 Im12 ~~ SAT_2 0.459 -0.014 -0.014 -0.045 -0.045
## 556 COI =~ Im16 0.453 -0.018 -0.030 -0.025 -0.025
## 557 PRODQUAL =~ C_REP1 0.445 0.022 0.016 0.021 0.021
## 558 BRAND =~ Im19 0.445 0.034 0.040 0.036 0.036
## 559 C_CR1 ~~ C_CR4 0.442 -0.240 -0.240 -0.200 -0.200
## 560 PROF =~ Im3 0.441 0.032 0.029 0.022 0.022
## 561 COM_A1 ~~ C_REP1 0.435 -0.013 -0.013 -0.034 -0.034
## 562 AFCOM =~ Im13 0.435 -0.023 -0.026 -0.021 -0.021
## 563 AFCOM =~ C_CR3 0.434 0.038 0.042 0.020 0.020
## 564 Im19 ~~ SAT_2 0.434 0.015 0.015 0.043 0.043
## 565 CHOICE =~ Im4 0.434 -0.015 -0.019 -0.014 -0.014
## 566 Im12 ~~ C_REP3 0.433 -0.008 -0.008 -0.039 -0.039
## 567 PROF =~ Im6 0.430 0.035 0.032 0.027 0.027
## 568 COI =~ COM_A3 0.429 0.020 0.032 0.020 0.020
## 569 CHOICE =~ Im11 0.426 -0.025 -0.032 -0.028 -0.028
## 570 Im1 ~~ Im16 0.420 -0.016 -0.016 -0.072 -0.072
## 571 CHOICE =~ Im3 0.410 -0.014 -0.019 -0.014 -0.014
## 572 SAT_1 ~~ C_REP2 0.407 -0.006 -0.006 -0.066 -0.066
## 573 Im6 ~~ SAT_3 0.403 -0.020 -0.020 -0.033 -0.033
## 574 Im13 ~~ Im6 0.401 0.016 0.016 0.038 0.038
## 575 AFCOM =~ Im4 0.399 -0.015 -0.016 -0.012 -0.012
## 576 RI =~ COM_A2 0.395 -0.050 -0.029 -0.018 -0.018
## 577 C_CR3 ~~ C_CR4 0.394 -0.226 -0.226 -0.165 -0.165
## 578 Im20 ~~ C_REP1 0.388 -0.012 -0.012 -0.033 -0.033
## 579 Im11 ~~ C_CR3 0.385 0.035 0.035 0.033 0.033
## 580 FRENCH =~ SAT_2 0.383 0.021 0.020 0.020 0.020
## 581 Im12 ~~ C_REP2 0.378 0.007 0.007 0.065 0.065
## 582 Im10 ~~ SAT_3 0.377 0.011 0.011 0.035 0.035
## 583 ATMOS ~ SAT 0.371 -0.052 -0.036 -0.036 -0.036
## 584 Im13 ~~ Im19 0.371 0.016 0.016 0.040 0.040
## 585 DECO =~ SAT_3 0.370 -0.023 -0.028 -0.025 -0.025
## 586 Im2 ~~ Im7 0.369 0.012 0.012 0.053 0.053
## 587 SAT_2 ~~ C_REP2 0.368 0.006 0.006 0.058 0.058
## 588 Im14 ~~ C_REP2 0.367 -0.004 -0.004 -0.078 -0.078
## 589 AFCOM =~ Im6 0.367 0.022 0.025 0.021 0.021
## 590 COM_A1 ~~ C_CR4 0.359 -0.034 -0.034 -0.033 -0.033
## 591 Im1 ~~ SAT_3 0.354 0.015 0.015 0.061 0.061
## 592 FOOD =~ Im3 0.352 -0.021 -0.017 -0.013 -0.013
## 593 Im6 ~~ COM_A2 0.352 0.020 0.020 0.033 0.033
## 594 ATMOS =~ Im16 0.351 -0.027 -0.033 -0.028 -0.028
## 595 Im5 ~~ Im22 0.351 0.022 0.022 0.033 0.033
## 596 PRODQUAL =~ COM_A1 0.350 0.040 0.028 0.020 0.020
## 597 C_REP2 ~~ C_CR3 0.348 0.012 0.012 0.056 0.056
## 598 Im17 ~~ COM_A2 0.346 -0.017 -0.017 -0.061 -0.061
## 599 Im5 ~~ Im17 0.344 0.015 0.015 0.056 0.056
## 600 Im11 ~~ C_REP3 0.343 0.009 0.009 0.028 0.028
## 601 COM_A3 ~~ SAT_1 0.342 0.018 0.018 0.037 0.037
## 602 CHOICE =~ COM_A4 0.338 -0.022 -0.029 -0.017 -0.017
## 603 Im3 ~~ COM_A2 0.336 -0.014 -0.014 -0.034 -0.034
## 604 Im3 ~~ COM_A1 0.336 -0.013 -0.013 -0.033 -0.033
## 605 Im17 ~~ C_CR1 0.333 -0.021 -0.021 -0.067 -0.067
## 606 FRENCH =~ Im3 0.330 -0.016 -0.016 -0.012 -0.012
## 607 Im6 ~~ C_CR1 0.326 0.024 0.024 0.034 0.034
## 608 Im11 ~~ COM_A1 0.321 -0.022 -0.022 -0.028 -0.028
## 609 COM_A4 ~~ SAT_2 0.316 0.018 0.018 0.034 0.034
## 610 SAT_2 ~~ C_CR1 0.314 -0.021 -0.021 -0.036 -0.036
## 611 FRENCH =~ COM_A4 0.312 0.031 0.030 0.018 0.018
## 612 Im3 ~~ Im13 0.310 0.010 0.010 0.035 0.035
## 613 Im19 ~~ C_CR3 0.309 0.025 0.025 0.035 0.035
## 614 CHOICE =~ C_CR3 0.303 -0.026 -0.035 -0.017 -0.017
## 615 Im3 ~~ SAT_2 0.303 -0.009 -0.009 -0.034 -0.034
## 616 Im13 ~~ Im7 0.303 -0.014 -0.014 -0.055 -0.055
## 617 Im5 ~~ C_REP2 0.302 -0.007 -0.007 -0.046 -0.046
## 618 Im17 ~~ Im7 0.301 -0.012 -0.012 -0.099 -0.099
## 619 Im18 ~~ SAT_1 0.296 -0.012 -0.012 -0.033 -0.033
## 620 Im19 ~~ C_CR1 0.292 0.023 0.023 0.036 0.036
## 621 Im21 ~~ Im13 0.288 -0.017 -0.017 -0.032 -0.032
## 622 AFCOM =~ Im7 0.287 -0.022 -0.024 -0.020 -0.020
## 623 AFCOM =~ Im14 0.284 0.010 0.011 0.013 0.013
## 624 COM_A1 ~~ C_CR1 0.282 -0.028 -0.028 -0.031 -0.031
## 625 Im4 ~~ Im14 0.279 0.005 0.005 0.058 0.058
## 626 Im5 ~~ Im20 0.279 0.020 0.020 0.028 0.028
## 627 COI =~ C_REP3 0.279 -0.006 -0.010 -0.017 -0.017
## 628 Im17 ~~ C_CR3 0.278 0.021 0.021 0.057 0.057
## 629 Im21 ~~ COM_A4 0.277 -0.023 -0.023 -0.029 -0.029
## 630 CHOICE =~ Im17 0.275 0.022 0.028 0.023 0.023
## 631 CHOICE =~ Im18 0.275 -0.021 -0.028 -0.020 -0.020
## 632 Im22 ~~ COM_A2 0.272 0.021 0.021 0.032 0.032
## 633 Im2 ~~ C_CR4 0.271 -0.019 -0.019 -0.029 -0.029
## 634 Im21 ~~ Im16 0.271 -0.019 -0.019 -0.028 -0.028
## 635 Im4 ~~ C_REP3 0.271 -0.005 -0.005 -0.038 -0.038
## 636 COI =~ Im6 0.265 -0.011 -0.018 -0.015 -0.015
## 637 Im7 ~~ SAT_2 0.262 -0.011 -0.011 -0.049 -0.049
## 638 CHOICE =~ Im6 0.256 -0.014 -0.019 -0.016 -0.016
## 639 Im17 ~~ SAT_2 0.247 0.009 0.009 0.054 0.054
## 640 Im20 ~~ Im19 0.247 0.016 0.016 0.031 0.031
## 641 COI =~ Im12 0.243 0.011 0.018 0.016 0.016
## 642 DECO =~ SAT_1 0.242 -0.015 -0.018 -0.018 -0.018
## 643 SAT =~ Im6 0.242 0.022 0.019 0.016 0.016
## 644 Im16 ~~ C_REP1 0.239 0.009 0.009 0.025 0.025
## 645 Im18 ~~ C_REP2 0.237 -0.006 -0.006 -0.043 -0.043
## 646 DECO =~ Im11 0.231 0.019 0.024 0.021 0.021
## 647 SAT_3 ~~ C_REP1 0.230 -0.009 -0.009 -0.024 -0.024
## 648 Im10 ~~ Im19 0.230 -0.007 -0.007 -0.032 -0.032
## 649 DECO =~ COM_A4 0.229 0.019 0.024 0.014 0.014
## 650 Im4 ~~ SAT_1 0.225 -0.007 -0.007 -0.043 -0.043
## 651 Im14 ~~ C_REP1 0.224 0.004 0.004 0.034 0.034
## 652 PROF =~ C_REP2 0.222 -0.011 -0.010 -0.016 -0.016
## 653 Im20 ~~ SAT_3 0.218 0.018 0.018 0.025 0.025
## 654 SAT_3 ~~ C_CR4 0.215 0.026 0.026 0.025 0.025
## 655 Im16 ~~ Im18 0.213 -0.014 -0.014 -0.025 -0.025
## 656 Im11 ~~ SAT_2 0.212 -0.013 -0.013 -0.025 -0.025
## 657 FOOD =~ COM_A4 0.212 -0.028 -0.023 -0.013 -0.013
## 658 PROF =~ SAT_3 0.209 -0.033 -0.030 -0.026 -0.026
## 659 Im21 ~~ SAT_1 0.208 0.012 0.012 0.028 0.028
## 660 Im21 ~~ SAT_2 0.207 -0.012 -0.012 -0.026 -0.026
## 661 Im22 ~~ Im17 0.206 0.012 0.012 0.053 0.053
## 662 Im5 ~~ SAT_1 0.205 -0.012 -0.012 -0.026 -0.026
## 663 AFCOM =~ SAT_3 0.204 0.020 0.023 0.020 0.020
## 664 Im3 ~~ C_REP2 0.199 -0.004 -0.004 -0.043 -0.043
## 665 Im4 ~~ C_REP2 0.198 0.004 0.004 0.058 0.058
## 666 SAT =~ COM_A4 0.197 0.030 0.026 0.015 0.015
## 667 PRODQUAL =~ C_CR3 0.195 -0.041 -0.029 -0.014 -0.014
## 668 Im12 ~~ C_CR3 0.194 0.019 0.019 0.029 0.029
## 669 SAT =~ Im7 0.191 0.021 0.018 0.015 0.015
## 670 Im11 ~~ C_CR1 0.188 -0.023 -0.023 -0.024 -0.024
## 671 Im13 ~~ COM_A1 0.187 0.014 0.014 0.025 0.025
## 672 Im6 ~~ C_REP1 0.185 -0.007 -0.007 -0.022 -0.022
## 673 RI =~ Im20 0.180 -0.036 -0.021 -0.014 -0.014
## 674 Im4 ~~ COM_A1 0.174 0.009 0.009 0.032 0.032
## 675 BRAND =~ Im21 0.174 -0.018 -0.022 -0.016 -0.016
## 676 AFCOM =~ Im18 0.174 -0.015 -0.017 -0.012 -0.012
## 677 Im5 ~~ COM_A3 0.173 -0.017 -0.017 -0.021 -0.021
## 678 AFCOM =~ SAT_1 0.171 -0.015 -0.016 -0.016 -0.016
## 679 Im21 ~~ Im2 0.169 0.010 0.010 0.022 0.022
## 680 Im21 ~~ Im19 0.169 -0.013 -0.013 -0.024 -0.024
## 681 Im16 ~~ C_REP2 0.168 -0.006 -0.006 -0.038 -0.038
## 682 COM_A4 ~~ C_CR1 0.167 0.024 0.024 0.025 0.025
## 683 COM_A2 ~~ C_REP3 0.164 -0.007 -0.007 -0.021 -0.021
## 684 Im20 ~~ Im11 0.164 0.016 0.016 0.021 0.021
## 685 Im22 ~~ C_CR3 0.164 0.023 0.023 0.026 0.026
## 686 ATMOS =~ SAT_1 0.163 0.011 0.014 0.014 0.014
## 687 RI =~ Im18 0.162 -0.027 -0.016 -0.011 -0.011
## 688 RI =~ Im17 0.162 0.027 0.016 0.013 0.013
## 689 DECO ~~ AFCOM 0.161 0.017 0.015 0.015 0.015
## 690 Im1 ~~ C_CR3 0.161 -0.015 -0.015 -0.045 -0.045
## 691 Im16 ~~ COM_A1 0.154 -0.015 -0.015 -0.021 -0.021
## 692 Im12 ~~ Im19 0.151 0.009 0.009 0.027 0.027
## 693 Im10 ~~ Im22 0.151 0.007 0.007 0.026 0.026
## 694 Im22 ~~ COM_A4 0.151 0.017 0.017 0.024 0.024
## 695 Im14 ~~ Im11 0.150 0.006 0.006 0.027 0.027
## 696 Im2 ~~ Im6 0.146 -0.008 -0.008 -0.020 -0.020
## 697 Im14 ~~ Im1 0.145 -0.004 -0.004 -0.058 -0.058
## 698 Im3 ~~ C_REP1 0.142 0.004 0.004 0.021 0.021
## 699 RI =~ C_CR3 0.140 0.041 0.024 0.012 0.012
## 700 Im21 ~~ C_REP2 0.139 -0.005 -0.005 -0.033 -0.033
## 701 SAT =~ Im10 0.138 -0.010 -0.008 -0.010 -0.010
## 702 FOOD =~ Im19 0.138 -0.024 -0.020 -0.017 -0.017
## 703 BRAND =~ SAT_1 0.137 -0.011 -0.013 -0.013 -0.013
## 704 Im4 ~~ Im13 0.137 -0.007 -0.007 -0.032 -0.032
## 705 FOOD =~ COM_A1 0.137 -0.021 -0.017 -0.012 -0.012
## 706 PROF =~ C_CR3 0.136 -0.027 -0.024 -0.012 -0.012
## 707 Im4 ~~ Im20 0.136 0.008 0.008 0.030 0.030
## 708 Im13 ~~ C_CR1 0.134 -0.016 -0.016 -0.024 -0.024
## 709 Im17 ~~ Im6 0.133 0.008 0.008 0.037 0.037
## 710 Im3 ~~ C_CR3 0.132 -0.012 -0.012 -0.022 -0.022
## 711 Im19 ~~ Im6 0.132 -0.009 -0.009 -0.021 -0.021
## 712 Im2 ~~ C_CR3 0.128 0.013 0.013 0.020 0.020
## 713 Im12 ~~ Im18 0.126 -0.009 -0.009 -0.022 -0.022
## 714 FOOD =~ Im4 0.124 -0.013 -0.010 -0.008 -0.008
## 715 RI =~ Im2 0.123 0.018 0.011 0.008 0.008
## 716 Im17 ~~ SAT_1 0.123 0.006 0.006 0.041 0.041
## 717 Im19 ~~ C_CR4 0.122 0.016 0.016 0.021 0.021
## 718 DECO ~ SAT 0.119 -0.057 -0.040 -0.040 -0.040
## 719 Im1 ~~ Im7 0.119 -0.007 -0.007 -0.063 -0.063
## 720 Im19 ~~ Im7 0.119 0.009 0.009 0.036 0.036
## 721 FRENCH =~ Im17 0.118 -0.014 -0.014 -0.011 -0.011
## 722 FRENCH =~ Im18 0.118 0.014 0.014 0.010 0.010
## 723 Im4 ~~ Im19 0.113 -0.006 -0.006 -0.030 -0.030
## 724 Im16 ~~ SAT_3 0.111 0.012 0.012 0.018 0.018
## 725 SAT =~ C_REP3 0.109 0.007 0.006 0.011 0.011
## 726 FOOD =~ Im21 0.109 0.018 0.015 0.011 0.011
## 727 COM_A3 ~~ C_CR4 0.109 -0.020 -0.020 -0.019 -0.019
## 728 Im18 ~~ C_CR3 0.109 -0.016 -0.016 -0.018 -0.018
## 729 AFCOM =~ Im19 0.108 0.012 0.013 0.012 0.012
## 730 AFCOM =~ Im1 0.108 -0.009 -0.010 -0.008 -0.008
## 731 COI =~ COM_A1 0.107 0.009 0.015 0.010 0.010
## 732 Im3 ~~ Im6 0.106 0.006 0.006 0.019 0.019
## 733 Im21 ~~ Im1 0.105 0.008 0.008 0.034 0.034
## 734 Im21 ~~ COM_A1 0.101 0.012 0.012 0.017 0.017
## 735 COI =~ Im7 0.100 -0.008 -0.013 -0.011 -0.011
## 736 Im17 ~~ C_CR4 0.098 0.012 0.012 0.033 0.033
## 737 CHOICE =~ SAT_3 0.098 0.012 0.016 0.014 0.014
## 738 COI =~ Im14 0.098 -0.004 -0.006 -0.007 -0.007
## 739 COI =~ Im10 0.098 0.004 0.006 0.007 0.007
## 740 FOOD =~ Im22 0.098 0.018 0.015 0.010 0.010
## 741 Im6 ~~ C_REP3 0.097 -0.004 -0.004 -0.016 -0.016
## 742 SAT =~ Im3 0.097 0.010 0.009 0.007 0.007
## 743 Im10 ~~ C_REP2 0.097 -0.002 -0.002 -0.031 -0.031
## 744 Im12 ~~ COM_A1 0.096 0.009 0.009 0.019 0.019
## 745 Im21 ~~ C_CR1 0.096 0.016 0.016 0.018 0.018
## 746 RI =~ Im6 0.094 0.019 0.011 0.010 0.010
## 747 C_REP3 ~~ C_CR1 0.093 0.007 0.007 0.017 0.017
## 748 ATMOS =~ Im6 0.092 -0.010 -0.013 -0.011 -0.011
## 749 ATMOS =~ Im7 0.092 0.012 0.015 0.012 0.012
## 750 AFCOM =~ Im10 0.092 -0.006 -0.006 -0.007 -0.007
## 751 DECO ~ AFCOM 0.090 0.015 0.013 0.013 0.013
## 752 ATMOS =~ SAT_3 0.086 -0.011 -0.014 -0.012 -0.012
## 753 Im5 ~~ COM_A4 0.085 -0.012 -0.012 -0.015 -0.015
## 754 Im5 ~~ Im18 0.084 0.009 0.009 0.014 0.014
## 755 AFCOM =~ Im17 0.084 0.009 0.010 0.008 0.008
## 756 Im10 ~~ C_REP1 0.082 0.002 0.002 0.016 0.016
## 757 Im4 ~~ Im21 0.080 0.006 0.006 0.022 0.022
## 758 FRENCH =~ C_CR3 0.077 -0.018 -0.018 -0.009 -0.009
## 759 DECO =~ Im21 0.077 -0.011 -0.014 -0.010 -0.010
## 760 Im6 ~~ SAT_2 0.076 -0.006 -0.006 -0.016 -0.016
## 761 Im22 ~~ COM_A3 0.075 0.012 0.012 0.017 0.017
## 762 FOOD =~ C_CR3 0.073 -0.021 -0.017 -0.008 -0.008
## 763 DECO =~ Im19 0.072 0.016 0.020 0.018 0.018
## 764 DECO =~ Im16 0.072 -0.016 -0.019 -0.016 -0.016
## 765 Im3 ~~ C_REP3 0.072 0.002 0.002 0.015 0.015
## 766 FRENCH =~ Im12 0.071 -0.011 -0.010 -0.009 -0.009
## 767 Im4 ~~ C_REP1 0.070 -0.003 -0.003 -0.020 -0.020
## 768 Im7 ~~ C_CR3 0.068 -0.011 -0.011 -0.025 -0.025
## 769 Im11 ~~ Im19 0.067 -0.008 -0.008 -0.014 -0.014
## 770 Im14 ~~ SAT_3 0.066 -0.004 -0.004 -0.019 -0.019
## 771 SAT =~ Im22 0.065 -0.015 -0.013 -0.008 -0.008
## 772 Im5 ~~ C_CR1 0.065 0.013 0.013 0.014 0.014
## 773 Im5 ~~ COM_A1 0.065 -0.010 -0.010 -0.013 -0.013
## 774 Im10 ~~ C_CR3 0.065 -0.006 -0.006 -0.016 -0.016
## 775 PROF =~ COM_A4 0.063 -0.015 -0.014 -0.008 -0.008
## 776 Im5 ~~ SAT_3 0.061 -0.009 -0.009 -0.012 -0.012
## 777 Im21 ~~ COM_A2 0.060 0.010 0.010 0.013 0.013
## 778 Im16 ~~ Im6 0.060 -0.007 -0.007 -0.013 -0.013
## 779 Im20 ~~ Im16 0.059 0.009 0.009 0.014 0.014
## 780 PROF =~ Im21 0.059 0.015 0.013 0.010 0.010
## 781 Im2 ~~ Im19 0.058 -0.005 -0.005 -0.014 -0.014
## 782 Im5 ~~ Im12 0.058 0.007 0.007 0.014 0.014
## 783 ATMOS =~ Im14 0.057 0.004 0.005 0.006 0.006
## 784 Im1 ~~ Im6 0.057 -0.005 -0.005 -0.025 -0.025
## 785 ATMOS =~ Im10 0.057 -0.004 -0.005 -0.006 -0.006
## 786 Im18 ~~ COM_A3 0.057 -0.009 -0.009 -0.013 -0.013
## 787 Im16 ~~ COM_A2 0.056 0.009 0.009 0.013 0.013
## 788 Im4 ~~ SAT_2 0.055 -0.004 -0.004 -0.020 -0.020
## 789 DECO =~ COM_A1 0.055 -0.009 -0.011 -0.007 -0.007
## 790 RI =~ C_CR1 0.054 -0.024 -0.014 -0.007 -0.007
## 791 Im14 ~~ COM_A1 0.054 0.004 0.004 0.017 0.017
## 792 Im10 ~~ Im1 0.054 -0.003 -0.003 -0.027 -0.027
## 793 COM_A2 ~~ C_REP1 0.052 0.005 0.005 0.012 0.012
## 794 Im20 ~~ C_CR1 0.050 -0.012 -0.012 -0.014 -0.014
## 795 RI =~ Im3 0.041 0.009 0.005 0.004 0.004
## 796 Im14 ~~ C_CR3 0.040 0.005 0.005 0.016 0.016
## 797 SAT_1 ~~ C_REP1 0.040 0.003 0.003 0.012 0.012
## 798 BRAND =~ C_CR3 0.039 -0.010 -0.012 -0.006 -0.006
## 799 RI =~ SAT_1 0.038 0.011 0.006 0.006 0.006
## 800 AFCOM =~ C_CR1 0.037 0.010 0.011 0.006 0.006
## 801 Im6 ~~ COM_A4 0.035 -0.007 -0.007 -0.010 -0.010
## 802 FOOD ~~ AFCOM 0.035 0.005 0.007 0.007 0.007
## 803 SAT =~ C_REP2 0.034 -0.004 -0.003 -0.005 -0.005
## 804 SAT_3 ~~ C_REP2 0.034 -0.003 -0.003 -0.016 -0.016
## 805 PRODQUAL =~ COM_A4 0.032 -0.013 -0.009 -0.006 -0.006
## 806 Im20 ~~ C_CR4 0.031 -0.010 -0.010 -0.010 -0.010
## 807 Im18 ~~ SAT_2 0.030 0.004 0.004 0.010 0.010
## 808 Im18 ~~ COM_A4 0.030 -0.006 -0.006 -0.009 -0.009
## 809 DECO =~ Im2 0.026 0.005 0.006 0.005 0.005
## 810 DECO =~ Im1 0.026 -0.006 -0.007 -0.005 -0.005
## 811 Im14 ~~ Im19 0.026 0.002 0.002 0.014 0.014
## 812 PROF ~ AFCOM 0.026 0.006 0.007 0.007 0.007
## 813 BRAND ~~ SAT 0.025 0.005 0.006 0.006 0.006
## 814 C_REP1 ~~ C_CR4 0.024 0.004 0.004 0.008 0.008
## 815 Im3 ~~ SAT_3 0.024 -0.004 -0.004 -0.009 -0.009
## 816 Im18 ~~ C_CR1 0.022 0.006 0.006 0.009 0.009
## 817 PROF =~ Im10 0.021 0.005 0.005 0.005 0.005
## 818 PROF =~ Im14 0.021 -0.005 -0.005 -0.006 -0.006
## 819 Im19 ~~ C_REP3 0.021 -0.002 -0.002 -0.008 -0.008
## 820 Im19 ~~ COM_A2 0.020 -0.005 -0.005 -0.009 -0.009
## 821 RI =~ SAT_3 0.020 0.011 0.006 0.006 0.006
## 822 BRAND ~~ AFCOM 0.020 -0.006 -0.005 -0.005 -0.005
## 823 RI =~ C_CR4 0.019 -0.015 -0.009 -0.004 -0.004
## 824 Im1 ~~ Im19 0.019 -0.003 -0.003 -0.017 -0.017
## 825 Im1 ~~ C_CR4 0.018 -0.005 -0.005 -0.015 -0.015
## 826 Im12 ~~ Im1 0.018 -0.003 -0.003 -0.017 -0.017
## 827 Im11 ~~ SAT_3 0.018 -0.005 -0.005 -0.006 -0.006
## 828 FRENCH =~ Im4 0.018 0.004 0.004 0.003 0.003
## 829 DECO =~ Im14 0.018 0.003 0.003 0.004 0.004
## 830 DECO =~ Im10 0.018 -0.003 -0.003 -0.004 -0.004
## 831 Im5 ~~ C_REP3 0.015 -0.002 -0.002 -0.006 -0.006
## 832 Im19 ~~ COM_A4 0.014 -0.004 -0.004 -0.007 -0.007
## 833 CHOICE =~ COM_A2 0.013 -0.004 -0.005 -0.003 -0.003
## 834 C_REP2 ~~ C_CR1 0.012 0.002 0.002 0.011 0.011
## 835 C_REP1 ~~ C_CR1 0.012 0.003 0.003 0.006 0.006
## 836 AFCOM =~ Im3 0.012 -0.003 -0.003 -0.002 -0.002
## 837 AFCOM =~ Im22 0.012 -0.006 -0.006 -0.004 -0.004
## 838 Im18 ~~ C_CR4 0.012 -0.005 -0.005 -0.006 -0.006
## 839 FOOD =~ Im17 0.011 0.005 0.004 0.003 0.003
## 840 FOOD =~ Im18 0.011 -0.005 -0.004 -0.003 -0.003
## 841 Im2 ~~ SAT_3 0.010 -0.003 -0.003 -0.005 -0.005
## 842 Im13 ~~ SAT_1 0.010 0.002 0.002 0.007 0.007
## 843 SAT_1 ~~ SAT_2 0.009 0.005 0.005 0.017 0.017
## 844 Im1 ~~ C_REP1 0.009 -0.001 -0.001 -0.009 -0.009
## 845 Im3 ~~ Im16 0.008 -0.002 -0.002 -0.005 -0.005
## 846 COI =~ Im21 0.008 0.002 0.004 0.003 0.003
## 847 Im21 ~~ COM_A3 0.008 -0.004 -0.004 -0.005 -0.005
## 848 CHOICE =~ Im7 0.007 0.003 0.003 0.003 0.003
## 849 COM_A3 ~~ C_CR1 0.007 0.005 0.005 0.005 0.005
## 850 FRENCH ~ AFCOM 0.006 0.006 0.007 0.007 0.007
## 851 Im11 ~~ Im16 0.006 -0.003 -0.003 -0.004 -0.004
## 852 COM_A2 ~~ C_REP2 0.006 0.001 0.001 0.007 0.007
## 853 Im3 ~~ Im21 0.005 -0.002 -0.002 -0.004 -0.004
## 854 SAT_2 ~~ C_CR4 0.005 0.003 0.003 0.004 0.004
## 855 COM_A4 ~~ C_REP2 0.005 -0.001 -0.001 -0.007 -0.007
## 856 PRODQUAL ~~ SAT 0.004 -0.001 -0.003 -0.003 -0.003
## 857 Im21 ~~ Im6 0.003 -0.002 -0.002 -0.003 -0.003
## 858 Im13 ~~ C_REP3 0.003 0.001 0.001 0.003 0.003
## 859 Im16 ~~ Im17 0.003 -0.001 -0.001 -0.006 -0.006
## 860 COM_A2 ~~ C_CR3 0.003 -0.003 -0.003 -0.003 -0.003
## 861 FOOD =~ SAT_1 0.003 -0.002 -0.002 -0.002 -0.002
## 862 FRENCH =~ Im10 0.002 0.002 0.002 0.002 0.002
## 863 FRENCH =~ Im14 0.002 -0.002 -0.002 -0.002 -0.002
## 864 Im22 ~~ C_CR4 0.002 0.003 0.003 0.003 0.003
## 865 Im16 ~~ C_CR3 0.002 -0.002 -0.002 -0.003 -0.003
## 866 PRODQUAL =~ Im3 0.002 0.002 0.001 0.001 0.001
## 867 PRODQUAL =~ Im21 0.001 0.002 0.002 0.001 0.001
## 868 Im6 ~~ C_CR3 0.001 -0.001 -0.001 -0.002 -0.002
## 869 BRAND =~ C_REP2 0.001 0.000 0.001 0.001 0.001
## 870 PRODQUAL =~ SAT_3 0.000 -0.001 -0.001 -0.001 -0.001
## 871 COI =~ Im18 0.000 0.000 -0.001 -0.001 -0.001
## 872 COI =~ Im17 0.000 0.000 0.001 0.001 0.001
## 873 Im4 ~~ SAT_3 0.000 0.000 0.000 -0.001 -0.001
## 874 Im2 ~~ COM_A2 0.000 0.000 0.000 -0.001 -0.001
## 875 Im13 ~~ C_CR4 0.000 0.001 0.001 0.001 0.001
## 876 FRENCH =~ C_REP3 0.000 0.000 0.000 0.000 0.000
## 877 Im19 ~~ COM_A3 0.000 0.000 0.000 0.001 0.001
## 878 Im18 ~~ SAT_3 0.000 0.000 0.000 -0.001 -0.001
## 879 FOOD =~ Im12 0.000 0.000 0.000 0.000 0.000
## 880 FRENCH =~ Im19 0.000 0.000 0.000 0.000 0.000
## 881 BRAND =~ COM_A1 0.000 0.000 0.000 0.000 0.000
## 882 DECO =~ C_CR3 0.000 0.000 0.000 0.000 0.000
## 883 FOOD =~ C_REP3 0.000 0.000 0.000 0.000 0.000
## 884 Im11 ~~ COM_A4 0.000 0.000 0.000 0.000 0.000
## 885 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
## 886 AFCOM =~ Im21 0.000 0.000 0.000 0.000 0.000
# missing Im8, Im15, Im9
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "
# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4
SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
RI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
COI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
"# # linear regression
# lm_SAT_1 <- lm (model_SAT_1, data = survey)
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 163 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 157
##
## Used Total
## Number of observations 523 553
## Number of missing patterns 116
##
## Model Test User Model:
##
## Test statistic 1893.114
## Degrees of freedom 499
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 12715.671
## Degrees of freedom 592
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.885
## Tucker-Lewis Index (TLI) 0.864
##
## Robust Comparative Fit Index (CFI) 0.887
## Robust Tucker-Lewis Index (TLI) 0.866
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -21220.663
## Loglikelihood unrestricted model (H1) -20274.106
##
## Akaike (AIC) 42755.327
## Bayesian (BIC) 43424.081
## Sample-size adjusted Bayesian (SABIC) 42925.726
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.073
## 90 Percent confidence interval - lower 0.070
## 90 Percent confidence interval - upper 0.077
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.001
##
## Robust RMSEA 0.074
## 90 Percent confidence interval - lower 0.070
## 90 Percent confidence interval - upper 0.077
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.141
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.247 0.942
## Im4 1.049 0.025 42.358 0.000 1.309 0.967
## Im5 0.802 0.034 23.246 0.000 1.000 0.757
## FOOD =~
## Im10 1.000 0.824 0.928
## Im14 0.999 0.035 28.444 0.000 0.822 0.952
## ATMOS =~
## Im20 1.000 1.252 0.843
## Im21 0.855 0.042 20.405 0.000 1.071 0.783
## Im22 1.084 0.047 23.227 0.000 1.357 0.887
## PRODQUAL =~
## Im11 1.000 0.715 0.620
## Im12 1.380 0.092 14.937 0.000 0.986 0.872
## Im13 1.446 0.104 13.967 0.000 1.034 0.858
## CHOICE =~
## Im1 1.000 1.300 0.978
## Im2 0.882 0.033 26.957 0.000 1.147 0.897
## PROF =~
## Im16 1.000 0.927 0.766
## Im19 1.035 0.058 17.947 0.000 0.959 0.846
## BRAND =~
## Im17 1.000 1.204 0.968
## Im18 0.996 0.042 23.603 0.000 1.199 0.857
## FRENCH =~
## Im6 1.000 0.977 0.812
## Im7 1.187 0.069 17.095 0.000 1.160 0.959
## AFCOM =~
## COM_A1 1.000 1.145 0.796
## COM_A2 1.173 0.056 21.035 0.000 1.343 0.836
## COM_A3 1.154 0.059 19.490 0.000 1.322 0.817
## COM_A4 1.297 0.064 20.376 0.000 1.485 0.849
## SAT =~
## SAT_1 1.000 0.881 0.863
## SAT_2 0.945 0.051 18.477 0.000 0.832 0.821
## SAT_3 0.840 0.055 15.374 0.000 0.740 0.658
## RI =~
## C_REP1 1.000 0.591 0.808
## C_REP2 0.982 0.045 21.741 0.000 0.581 0.935
## C_REP3 0.719 0.038 18.681 0.000 0.425 0.764
## COI =~
## C_CR1 1.000 1.695 0.853
## C_CR3 1.029 0.052 19.721 0.000 1.743 0.831
## C_CR4 0.958 0.050 19.155 0.000 1.623 0.807
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SAT ~
## DECO -0.079 0.045 -1.764 0.078 -0.113 -0.113
## CHOICE 0.126 0.040 3.138 0.002 0.185 0.185
## PROF 0.549 0.083 6.643 0.000 0.577 0.577
## AFCOM ~
## ATMOS 0.424 0.050 8.553 0.000 0.464 0.464
## PRODQUAL -0.033 0.081 -0.409 0.682 -0.021 -0.021
## FRENCH 0.240 0.055 4.364 0.000 0.205 0.205
## RI ~
## SAT 0.192 0.045 4.232 0.000 0.286 0.286
## AFCOM 0.183 0.030 6.101 0.000 0.355 0.355
## DECO 0.006 0.029 0.190 0.850 0.012 0.012
## FOOD 0.012 0.049 0.241 0.809 0.016 0.016
## ATMOS 0.040 0.029 1.369 0.171 0.085 0.085
## PRODQUAL 0.110 0.052 2.103 0.035 0.133 0.133
## CHOICE -0.018 0.027 -0.674 0.500 -0.041 -0.041
## PROF -0.023 0.066 -0.346 0.730 -0.036 -0.036
## BRAND 0.008 0.030 0.256 0.798 0.016 0.016
## FRENCH -0.034 0.039 -0.882 0.378 -0.057 -0.057
## Im8 0.050 0.036 1.371 0.170 0.085 0.089
## Im15 -0.001 0.030 -0.042 0.966 -0.002 -0.003
## Im9 -0.047 0.022 -2.091 0.037 -0.079 -0.107
## COI ~
## SAT -0.351 0.137 -2.571 0.010 -0.183 -0.183
## AFCOM 0.531 0.093 5.725 0.000 0.359 0.359
## DECO 0.016 0.093 0.174 0.862 0.012 0.012
## FOOD -0.059 0.155 -0.379 0.705 -0.028 -0.028
## ATMOS 0.146 0.093 1.569 0.117 0.108 0.108
## PRODQUAL 0.248 0.167 1.491 0.136 0.105 0.105
## CHOICE -0.000 0.089 -0.000 1.000 -0.000 -0.000
## PROF -0.194 0.208 -0.932 0.351 -0.106 -0.106
## BRAND 0.036 0.097 0.370 0.712 0.025 0.025
## FRENCH -0.115 0.125 -0.921 0.357 -0.066 -0.066
## Im8 -0.013 0.116 -0.113 0.910 -0.008 -0.008
## Im15 -0.057 0.098 -0.586 0.558 -0.034 -0.040
## Im9 -0.014 0.071 -0.198 0.843 -0.008 -0.011
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.425 0.052 8.163 0.000 0.414 0.414
## ATMOS 0.740 0.084 8.814 0.000 0.473 0.473
## PRODQUAL 0.419 0.053 7.877 0.000 0.470 0.470
## CHOICE 0.732 0.081 8.987 0.000 0.451 0.451
## PROF 0.770 0.073 10.478 0.000 0.666 0.666
## BRAND 0.785 0.079 9.986 0.000 0.523 0.523
## FRENCH 0.411 0.065 6.291 0.000 0.337 0.337
## FOOD ~~
## ATMOS 0.311 0.052 5.948 0.000 0.301 0.301
## PRODQUAL 0.264 0.035 7.461 0.000 0.448 0.448
## CHOICE 0.311 0.051 6.052 0.000 0.290 0.290
## PROF 0.401 0.045 8.821 0.000 0.526 0.526
## BRAND 0.322 0.049 6.639 0.000 0.325 0.325
## FRENCH 0.473 0.049 9.744 0.000 0.588 0.588
## ATMOS ~~
## PRODQUAL 0.389 0.055 7.109 0.000 0.435 0.435
## CHOICE 0.764 0.086 8.868 0.000 0.469 0.469
## PROF 0.573 0.070 8.220 0.000 0.494 0.494
## BRAND 0.796 0.082 9.660 0.000 0.528 0.528
## FRENCH 0.409 0.066 6.248 0.000 0.334 0.334
## PRODQUAL ~~
## CHOICE 0.446 0.056 8.029 0.000 0.480 0.480
## PROF 0.363 0.045 7.990 0.000 0.548 0.548
## BRAND 0.483 0.055 8.838 0.000 0.561 0.561
## FRENCH 0.219 0.039 5.620 0.000 0.313 0.313
## CHOICE ~~
## PROF 0.732 0.074 9.915 0.000 0.608 0.608
## BRAND 0.806 0.080 10.029 0.000 0.515 0.515
## FRENCH 0.275 0.062 4.471 0.000 0.217 0.217
## PROF ~~
## BRAND 0.680 0.068 10.004 0.000 0.609 0.609
## FRENCH 0.356 0.053 6.662 0.000 0.393 0.393
## BRAND ~~
## FRENCH 0.376 0.063 5.996 0.000 0.319 0.319
## .RI ~~
## .COI -0.025 0.039 -0.626 0.532 -0.033 -0.033
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.983 0.058 85.742 0.000 4.983 3.762
## .Im4 4.995 0.059 84.296 0.000 4.995 3.692
## .Im5 5.049 0.058 86.541 0.000 5.049 3.823
## .Im10 6.093 0.039 156.809 0.000 6.093 6.865
## .Im14 6.139 0.038 161.825 0.000 6.139 7.108
## .Im20 4.705 0.065 72.271 0.000 4.705 3.166
## .Im21 5.163 0.060 86.177 0.000 5.163 3.775
## .Im22 4.305 0.067 63.985 0.000 4.305 2.813
## .Im11 5.652 0.051 111.583 0.000 5.652 4.907
## .Im12 5.667 0.050 113.799 0.000 5.667 5.010
## .Im13 5.451 0.053 103.064 0.000 5.451 4.525
## .Im1 4.808 0.058 82.563 0.000 4.808 3.618
## .Im2 4.877 0.056 86.958 0.000 4.877 3.814
## .Im16 5.150 0.053 96.412 0.000 5.150 4.259
## .Im19 5.158 0.050 103.703 0.000 5.158 4.551
## .Im17 5.044 0.054 92.559 0.000 5.044 4.056
## .Im18 4.603 0.062 74.674 0.000 4.603 3.289
## .Im6 5.821 0.053 110.236 0.000 5.821 4.835
## .Im7 5.759 0.053 108.103 0.000 5.759 4.760
## .COM_A1 4.301 0.063 68.014 0.000 4.301 2.990
## .COM_A2 3.906 0.070 55.416 0.000 3.906 2.432
## .COM_A3 3.556 0.071 49.898 0.000 3.556 2.197
## .COM_A4 3.482 0.077 45.431 0.000 3.482 1.992
## .SAT_1 5.345 0.045 119.553 0.000 5.345 5.236
## .SAT_2 5.483 0.045 123.186 0.000 5.483 5.410
## .SAT_3 5.476 0.050 108.497 0.000 5.476 4.864
## .C_REP1 4.221 0.274 15.421 0.000 4.221 5.767
## .C_REP2 4.451 0.268 16.591 0.000 4.451 7.163
## .C_REP3 4.630 0.197 23.504 0.000 4.630 8.315
## .C_CR1 3.142 0.875 3.590 0.000 3.142 1.581
## .C_CR3 3.747 0.900 4.161 0.000 3.747 1.786
## .C_CR4 3.235 0.838 3.860 0.000 3.235 1.609
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## .AFCOM 0.000 0.000 0.000
## .SAT 0.000 0.000 0.000
## .RI 0.000 0.000 0.000
## .COI 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.198 0.025 8.033 0.000 0.198 0.113
## .Im4 0.118 0.025 4.748 0.000 0.118 0.064
## .Im5 0.744 0.050 14.899 0.000 0.744 0.427
## .Im10 0.109 0.020 5.594 0.000 0.109 0.139
## .Im14 0.070 0.019 3.699 0.000 0.070 0.093
## .Im20 0.640 0.059 10.906 0.000 0.640 0.290
## .Im21 0.724 0.058 12.579 0.000 0.724 0.387
## .Im22 0.499 0.060 8.306 0.000 0.499 0.213
## .Im11 0.816 0.057 14.441 0.000 0.816 0.615
## .Im12 0.306 0.039 7.864 0.000 0.306 0.240
## .Im13 0.383 0.045 8.592 0.000 0.383 0.264
## .Im1 0.076 0.049 1.545 0.122 0.076 0.043
## .Im2 0.320 0.043 7.461 0.000 0.320 0.196
## .Im16 0.604 0.051 11.825 0.000 0.604 0.413
## .Im19 0.365 0.044 8.348 0.000 0.365 0.284
## .Im17 0.097 0.046 2.102 0.036 0.097 0.063
## .Im18 0.520 0.056 9.278 0.000 0.520 0.266
## .Im6 0.495 0.055 8.939 0.000 0.495 0.341
## .Im7 0.119 0.065 1.839 0.066 0.119 0.081
## .COM_A1 0.758 0.060 12.599 0.000 0.758 0.366
## .COM_A2 0.774 0.067 11.530 0.000 0.774 0.300
## .COM_A3 0.873 0.072 12.207 0.000 0.873 0.333
## .COM_A4 0.851 0.077 11.114 0.000 0.851 0.278
## .SAT_1 0.266 0.035 7.682 0.000 0.266 0.255
## .SAT_2 0.334 0.035 9.624 0.000 0.334 0.325
## .SAT_3 0.719 0.053 13.621 0.000 0.719 0.567
## .C_REP1 0.186 0.016 11.320 0.000 0.186 0.347
## .C_REP2 0.049 0.011 4.658 0.000 0.049 0.127
## .C_REP3 0.129 0.009 13.621 0.000 0.129 0.417
## .C_CR1 1.076 0.119 9.064 0.000 1.076 0.273
## .C_CR3 1.363 0.134 10.155 0.000 1.363 0.310
## .C_CR4 1.412 0.128 11.025 0.000 1.412 0.349
## DECO 1.556 0.110 14.093 0.000 1.000 1.000
## FOOD 0.678 0.052 13.130 0.000 1.000 1.000
## ATMOS 1.568 0.138 11.391 0.000 1.000 1.000
## PRODQUAL 0.511 0.070 7.300 0.000 1.000 1.000
## CHOICE 1.690 0.120 14.110 0.000 1.000 1.000
## PROF 0.858 0.090 9.573 0.000 1.000 1.000
## BRAND 1.450 0.106 13.655 0.000 1.000 1.000
## FRENCH 0.955 0.096 9.930 0.000 1.000 1.000
## .AFCOM 0.904 0.092 9.795 0.000 0.689 0.689
## .SAT 0.462 0.051 9.139 0.000 0.595 0.595
## .RI 0.232 0.022 10.544 0.000 0.663 0.663
## .COI 2.332 0.219 10.636 0.000 0.812 0.812
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI Im8
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.385 NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 Im9
## Im3 NaN NaN
## Im4 NaN NaN
## Im5 NaN NaN
## Im10 NaN NaN
## Im14 NaN NaN
## Im20 NaN NaN
## Im21 NaN NaN
## Im22 NaN NaN
## Im11 NaN NaN
## Im12 NaN NaN
## Im13 NaN NaN
## Im1 NaN NaN
## Im2 NaN NaN
## Im16 NaN NaN
## Im19 NaN NaN
## Im17 NaN NaN
## Im18 NaN NaN
## Im6 NaN NaN
## Im7 NaN NaN
## COM_A1 NaN NaN
## COM_A2 NaN NaN
## COM_A3 NaN NaN
## COM_A4 NaN NaN
## SAT_1 NaN NaN
## SAT_2 NaN NaN
## SAT_3 NaN NaN
## C_REP1 NaN NaN
## C_REP2 NaN NaN
## C_REP3 NaN NaN
## C_CR1 NaN NaN
## C_CR3 NaN NaN
## C_CR4 NaN NaN
## Im8 NaN NaN
## Im15 NaN NaN
## Im9 NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 Im15 Im9
## DECO NaN NaN NaN
## FOOD NaN NaN NaN
## ATMOS NaN NaN NaN
## PRODQUAL NaN NaN NaN
## CHOICE NaN NaN NaN
## PROF NaN NaN NaN
## BRAND NaN NaN NaN
## FRENCH NaN NaN NaN
## AFCOM NaN NaN NaN
## SAT NaN NaN NaN
## RI NaN NaN NaN
## COI NaN NaN NaN
## Im8 NaN NaN NaN
## Im15 NaN NaN NaN
## Im9 NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 Im15 Im9
## DECO NaN NaN NaN
## FOOD NaN NaN NaN
## ATMOS NaN NaN NaN
## PRODQUAL NaN NaN NaN
## CHOICE NaN NaN NaN
## PROF NaN NaN NaN
## BRAND NaN NaN NaN
## FRENCH NaN NaN NaN
## AFCOM NaN NaN NaN
## SAT NaN NaN NaN
## RI NaN NaN NaN
## COI NaN NaN NaN
## Im8 NaN NaN NaN
## Im15 NaN NaN NaN
## Im9 NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI
## DECO 1.000
## FOOD NaN 1.000
## ATMOS NaN NaN 1.000
## PRODQUAL NaN NaN NaN 1.000
## CHOICE NaN NaN NaN NaN 1.000
## PROF NaN NaN NaN NaN NaN 1.000
## BRAND NaN NaN NaN NaN NaN NaN 1.000
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1.000
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI
## COI 0.812
## Im8 NaN 1.000
## Im15 NaN NaN 1.000
## Im9 NaN NaN NaN 1.000
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## FOOD 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## ATMOS 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## PRODQUAL 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## CHOICE 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## PROF 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## BRAND 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## FRENCH 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## AFCOM 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## SAT 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## RI 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## COI 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im8 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im15 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## Im9 0.7986898 0.8840285 0.703334 0.6271894 0.8805849 0.6515617 0.8358394
## FRENCH AFCOM SAT RI COI Im8 Im15 Im9
## DECO 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## FOOD 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## ATMOS 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## PRODQUAL 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## CHOICE 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## PROF 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## BRAND 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## FRENCH 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## AFCOM 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## SAT 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## RI 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## COI 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## Im8 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## Im15 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
## Im9 0.7887533 0.680406 0.6175005 0.7029673 0.689651 1 1 1
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO 1.000
## FOOD 0.414 1.000
## ATMOS 0.473 0.301 1.000
## PRODQUAL 0.470 0.448 0.435 1.000
## CHOICE 0.451 0.290 0.469 0.480 1.000
## PROF 0.666 0.526 0.494 0.548 0.608 1.000
## BRAND 0.523 0.325 0.528 0.561 0.515 0.609 1.000
## FRENCH 0.337 0.588 0.334 0.313 0.217 0.393 0.319 1.000
## AFCOM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.689
## SAT 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.595
## RI 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## COI 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im15 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## RI COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI 0.663
## COI -0.033 0.812
## Im8 0.000 0.000 1.000
## Im15 0.000 0.000 0.342 1.000
## Im9 0.000 0.000 0.442 0.397 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN .
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN .
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI .
## COI NaN .
## Im8 NaN NaN .
## Im15 NaN NaN NaN .
## Im9 NaN NaN NaN NaN .
arrange(modificationindices(SEM_fit),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im15 ~ CHOICE 182.606 0.497 0.646 0.542 0.542
## 2 Im8 ~ FOOD 165.135 0.649 0.534 0.509 0.509
## 3 Im15 ~ PROF 142.369 0.652 0.604 0.507 0.507
## 4 Im8 ~ FRENCH 131.378 0.492 0.481 0.458 0.458
## 5 Im15 ~ BRAND 87.499 0.374 0.451 0.378 0.378
## 6 Im15 ~ RI 86.137 1.347 0.797 0.669 0.669
## 7 Im15 ~ PRODQUAL 85.339 0.647 0.463 0.388 0.388
## 8 Im15 ~ SAT 73.509 0.492 0.433 0.363 0.363
## 9 Im15 ~ ATMOS 70.517 0.332 0.416 0.349 0.349
## 10 Im15 ~ DECO 69.835 0.321 0.400 0.336 0.336
## 11 FOOD ~ Im8 63.988 0.217 0.264 0.277 0.264
## 12 FRENCH ~ Im8 60.204 0.269 0.275 0.289 0.275
## 13 AFCOM =~ C_REP1 55.975 0.174 0.200 0.273 0.273
## 14 FRENCH ~ Im9 49.676 0.189 0.193 0.263 0.193
## 15 C_REP2 ~~ C_REP3 49.318 0.103 0.103 1.291 1.291
## 16 AFCOM ~ SAT 40.895 0.403 0.310 0.310 0.310
## 17 SAT ~ AFCOM 40.627 0.222 0.288 0.288 0.288
## 18 CHOICE ~ Im15 38.544 0.236 0.182 0.217 0.182
## 19 AFCOM ~ COI 37.183 -0.808 -1.196 -1.196 -1.196
## 20 AFCOM ~~ SAT 34.958 0.217 0.335 0.335 0.335
## 21 AFCOM ~ RI 34.443 1.874 0.968 0.968 0.968
## 22 SAT ~ RI 31.869 0.895 0.601 0.601 0.601
## 23 Im9 ~ BRAND 31.649 0.245 0.295 0.217 0.217
## 24 Im9 ~ FRENCH 31.256 0.304 0.297 0.218 0.218
## 25 COM_A1 ~~ COM_A2 30.349 0.284 0.284 0.371 0.371
## 26 Im9 ~ PRODQUAL 27.722 0.402 0.287 0.211 0.211
## 27 SAT ~ COI 26.144 0.287 0.552 0.552 0.552
## 28 Im15 ~ AFCOM 24.017 0.212 0.242 0.203 0.203
## 29 ATMOS =~ C_REP1 21.866 0.095 0.119 0.162 0.162
## 30 Im8 ~ PROF 19.101 0.205 0.190 0.181 0.181
## 31 BRAND =~ Im13 19.101 0.197 0.237 0.196 0.196
## 32 Im11 ~~ Im13 18.857 -0.182 -0.182 -0.326 -0.326
## 33 PROF ~ Im15 18.511 0.113 0.122 0.146 0.122
## 34 RI =~ SAT_2 17.237 0.269 0.159 0.157 0.157
## 35 CHOICE =~ Im20 16.539 -0.162 -0.211 -0.142 -0.142
## 36 PRODQUAL ~ Im9 15.822 0.078 0.109 0.149 0.109
## 37 RI =~ Im22 14.652 -0.331 -0.196 -0.128 -0.128
## 38 AFCOM =~ C_REP2 14.550 -0.076 -0.087 -0.139 -0.139
## 39 Im21 ~~ Im22 14.329 -0.237 -0.237 -0.394 -0.394
## 40 BRAND =~ Im12 14.102 -0.160 -0.193 -0.171 -0.171
## 41 Im8 ~ RI 13.989 0.467 0.276 0.263 0.263
## 42 Im8 ~ AFCOM 13.785 0.138 0.158 0.151 0.151
## 43 C_REP1 ~~ C_REP3 13.547 -0.049 -0.049 -0.318 -0.318
## 44 COM_A3 ~~ C_REP1 13.032 0.080 0.080 0.197 0.197
## 45 FOOD =~ Im11 12.844 0.217 0.179 0.155 0.155
## 46 CHOICE =~ Im13 12.827 0.130 0.169 0.140 0.140
## 47 SAT =~ COM_A3 12.554 0.207 0.183 0.113 0.113
## 48 AFCOM =~ SAT_2 12.377 0.102 0.116 0.115 0.115
## 49 Im8 ~ SAT 12.277 0.173 0.152 0.145 0.145
## 50 Im21 ~~ C_REP3 12.244 0.056 0.056 0.183 0.183
## 51 Im9 ~ ATMOS 12.056 0.150 0.187 0.138 0.138
## 52 SAT ~ FRENCH 11.829 0.148 0.164 0.164 0.164
## 53 AFCOM =~ C_REP3 11.813 -0.064 -0.074 -0.133 -0.133
## 54 Im9 ~ RI 11.217 0.529 0.313 0.230 0.230
## 55 PROF =~ COM_A3 11.112 0.195 0.180 0.111 0.111
## 56 BRAND ~ Im9 10.995 0.098 0.081 0.111 0.081
## 57 Im11 ~~ Im12 10.597 0.130 0.130 0.260 0.260
## 58 Im8 ~ DECO 10.547 0.107 0.134 0.127 0.127
## 59 Im13 ~~ Im1 10.493 0.068 0.068 0.400 0.400
## 60 ATMOS =~ Im12 10.450 -0.115 -0.144 -0.127 -0.127
## 61 C_REP1 ~~ C_REP2 10.416 -0.072 -0.072 -0.756 -0.756
## 62 COM_A1 ~~ COM_A4 10.164 -0.180 -0.180 -0.224 -0.224
## 63 PRODQUAL ~ Im15 10.076 0.071 0.099 0.119 0.099
## 64 FRENCH ~ COI 10.002 -0.359 -0.623 -0.623 -0.623
## 65 PRODQUAL ~ RI 9.997 -0.553 -0.458 -0.458 -0.458
## 66 CHOICE =~ C_REP1 9.925 0.055 0.072 0.098 0.098
## 67 AFCOM =~ Im11 9.855 0.126 0.144 0.125 0.125
## 68 SAT =~ C_CR4 9.826 0.239 0.211 0.105 0.105
## 69 PRODQUAL =~ C_CR4 9.641 0.289 0.207 0.103 0.103
## 70 ATMOS =~ C_REP3 9.610 -0.051 -0.064 -0.114 -0.114
## 71 CHOICE =~ Im12 9.376 -0.105 -0.137 -0.121 -0.121
## 72 BRAND =~ Im20 9.366 -0.142 -0.171 -0.115 -0.115
## 73 COM_A3 ~~ COM_A4 9.167 0.194 0.194 0.225 0.225
## 74 Im13 ~~ Im17 9.136 0.068 0.068 0.354 0.354
## 75 CHOICE =~ C_REP3 9.111 -0.043 -0.056 -0.101 -0.101
## 76 RI =~ Im21 9.083 0.250 0.148 0.108 0.108
## 77 PROF ~ SAT 9.064 -0.330 -0.313 -0.313 -0.313
## 78 PROF ~~ SAT 9.064 -0.152 -0.242 -0.242 -0.242
## 79 Im16 ~~ Im19 9.064 0.287 0.287 0.612 0.612
## 80 ATMOS =~ C_CR4 8.951 0.162 0.203 0.101 0.101
## 81 COI =~ SAT_2 8.908 0.061 0.103 0.101 0.101
## 82 FOOD ~ RI 8.883 0.425 0.305 0.305 0.305
## 83 Im10 ~~ Im6 8.775 -0.042 -0.042 -0.182 -0.182
## 84 AFCOM ~ PROF 8.643 0.225 0.182 0.182 0.182
## 85 Im4 ~~ Im17 8.327 -0.044 -0.044 -0.415 -0.415
## 86 DECO =~ COM_A3 8.160 0.115 0.144 0.089 0.089
## 87 FRENCH =~ C_REP1 8.002 0.066 0.064 0.088 0.088
## 88 SAT ~ FOOD 7.987 0.159 0.149 0.149 0.149
## 89 RI =~ COM_A1 7.971 0.251 0.148 0.103 0.103
## 90 Im19 ~~ C_REP1 7.883 -0.045 -0.045 -0.171 -0.171
## 91 COI =~ C_REP1 7.851 0.038 0.064 0.087 0.087
## 92 Im1 ~~ SAT_2 7.828 -0.053 -0.053 -0.332 -0.332
## 93 PRODQUAL =~ C_CR1 7.719 -0.249 -0.178 -0.090 -0.090
## 94 FOOD =~ Im6 7.603 -0.303 -0.249 -0.207 -0.207
## 95 BRAND =~ Im22 7.593 0.131 0.158 0.103 0.103
## 96 AFCOM ~ CHOICE 7.579 0.124 0.140 0.140 0.140
## 97 SAT =~ C_REP1 7.571 0.081 0.071 0.097 0.097
## 98 DECO =~ Im20 7.454 -0.114 -0.143 -0.096 -0.096
## 99 BRAND =~ COM_A3 7.093 0.113 0.136 0.084 0.084
## 100 COM_A4 ~~ SAT_1 7.080 0.084 0.084 0.176 0.176
## 101 Im22 ~~ C_REP3 7.019 -0.042 -0.042 -0.163 -0.163
## 102 PRODQUAL ~ COI 7.005 -0.212 -0.503 -0.503 -0.503
## 103 SAT ~ Im8 6.880 0.088 0.099 0.104 0.099
## 104 DECO ~~ SAT 6.878 -0.342 -0.403 -0.403 -0.403
## 105 DECO ~ SAT 6.877 -0.740 -0.523 -0.523 -0.523
## 106 DECO =~ C_CR1 6.855 -0.128 -0.160 -0.080 -0.080
## 107 DECO =~ C_REP1 6.832 0.048 0.060 0.081 0.081
## 108 ATMOS ~ COI 6.795 -0.412 -0.558 -0.558 -0.558
## 109 Im9 ~ DECO 6.761 0.109 0.135 0.100 0.100
## 110 Im15 ~ COI 6.706 0.178 0.301 0.253 0.253
## 111 BRAND =~ Im7 6.608 -0.103 -0.123 -0.102 -0.102
## 112 Im3 ~~ Im1 6.578 -0.038 -0.038 -0.308 -0.308
## 113 PROF =~ C_CR4 6.569 0.185 0.171 0.085 0.085
## 114 ATMOS =~ Im11 6.553 0.105 0.131 0.114 0.114
## 115 Im10 ~~ Im7 6.452 0.037 0.037 0.329 0.329
## 116 Im10 ~~ Im16 6.282 0.041 0.041 0.160 0.160
## 117 RI =~ Im12 6.272 -0.166 -0.098 -0.087 -0.087
## 118 Im20 ~~ Im21 6.250 0.142 0.142 0.208 0.208
## 119 SAT =~ Im12 6.193 -0.112 -0.099 -0.088 -0.088
## 120 COM_A2 ~~ COM_A3 6.190 -0.145 -0.145 -0.177 -0.177
## 121 BRAND =~ Im6 6.136 0.084 0.101 0.084 0.084
## 122 BRAND =~ C_CR4 6.117 0.131 0.158 0.079 0.079
## 123 FOOD =~ COM_A3 6.048 0.151 0.124 0.077 0.077
## 124 FRENCH =~ Im22 6.042 0.125 0.122 0.080 0.080
## 125 BRAND =~ Im4 6.035 -0.067 -0.081 -0.060 -0.060
## 126 PRODQUAL =~ Im5 6.012 0.170 0.122 0.092 0.092
## 127 PRODQUAL ~ AFCOM 5.971 -0.136 -0.219 -0.219 -0.219
## 128 PRODQUAL ~~ AFCOM 5.971 -0.123 -0.181 -0.181 -0.181
## 129 PROF =~ C_REP3 5.927 -0.054 -0.050 -0.090 -0.090
## 130 RI =~ Im14 5.920 0.086 0.051 0.059 0.059
## 131 FRENCH =~ Im16 5.903 -0.125 -0.122 -0.101 -0.101
## 132 Im9 ~ COI 5.894 0.182 0.308 0.226 0.226
## 133 SAT_1 ~~ SAT_3 5.829 0.098 0.098 0.224 0.224
## 134 DECO =~ C_CR4 5.813 0.122 0.153 0.076 0.076
## 135 CHOICE =~ Im5 5.813 0.085 0.111 0.084 0.084
## 136 FOOD =~ Im7 5.805 0.319 0.263 0.217 0.217
## 137 DECO =~ Im7 5.790 -0.094 -0.117 -0.097 -0.097
## 138 SAT_2 ~~ SAT_3 5.753 -0.092 -0.092 -0.187 -0.187
## 139 ATMOS =~ COM_A1 5.615 -0.107 -0.134 -0.093 -0.093
## 140 AFCOM =~ Im12 5.592 -0.077 -0.089 -0.078 -0.078
## 141 Im10 ~~ Im13 5.573 -0.033 -0.033 -0.163 -0.163
## 142 DECO =~ Im22 5.482 0.100 0.125 0.081 0.081
## 143 Im9 ~ AFCOM 5.441 0.110 0.126 0.092 0.092
## 144 DECO =~ C_REP3 5.433 -0.035 -0.043 -0.078 -0.078
## 145 Im10 ~~ COM_A2 5.414 0.043 0.043 0.148 0.148
## 146 FRENCH =~ Im20 5.341 -0.115 -0.112 -0.076 -0.076
## 147 Im14 ~~ Im16 5.332 -0.037 -0.037 -0.178 -0.178
## 148 Im13 ~~ Im2 5.238 -0.048 -0.048 -0.137 -0.137
## 149 BRAND =~ Im5 5.235 0.093 0.112 0.085 0.085
## 150 Im20 ~~ Im17 5.217 -0.061 -0.061 -0.246 -0.246
## 151 PROF =~ Im20 5.188 -0.143 -0.132 -0.089 -0.089
## 152 ATMOS =~ Im5 5.177 0.089 0.111 0.084 0.084
## 153 FOOD =~ C_REP1 5.072 0.062 0.051 0.070 0.070
## 154 DECO =~ Im6 5.061 0.075 0.093 0.077 0.077
## 155 PROF =~ SAT_2 5.028 0.134 0.124 0.123 0.123
## 156 FOOD =~ Im13 4.954 -0.124 -0.102 -0.085 -0.085
## 157 Im15 ~ FOOD 4.900 0.130 0.107 0.090 0.090
## 158 PROF =~ Im12 4.838 -0.132 -0.122 -0.108 -0.108
## 159 ATMOS ~ AFCOM 4.783 -0.263 -0.241 -0.241 -0.241
## 160 ATMOS ~~ AFCOM 4.782 -0.238 -0.200 -0.200 -0.200
## 161 DECO =~ Im18 4.776 0.097 0.120 0.086 0.086
## 162 DECO =~ Im17 4.776 -0.097 -0.121 -0.097 -0.097
## 163 SAT_3 ~~ C_CR3 4.759 -0.123 -0.123 -0.125 -0.125
## 164 FRENCH ~ SAT 4.717 0.140 0.126 0.126 0.126
## 165 FRENCH ~~ SAT 4.717 0.065 0.097 0.097 0.097
## 166 BRAND =~ C_REP3 4.703 -0.034 -0.041 -0.074 -0.074
## 167 FRENCH =~ C_REP2 4.701 -0.042 -0.041 -0.065 -0.065
## 168 Im19 ~~ C_REP2 4.680 0.027 0.027 0.199 0.199
## 169 Im20 ~~ Im6 4.664 -0.068 -0.068 -0.120 -0.120
## 170 C_REP2 ~~ C_CR4 4.629 -0.046 -0.046 -0.174 -0.174
## 171 COM_A3 ~~ C_REP2 4.626 -0.035 -0.035 -0.171 -0.171
## 172 Im3 ~~ COM_A4 4.625 0.055 0.055 0.134 0.134
## 173 COM_A1 ~~ SAT_3 4.601 0.084 0.084 0.114 0.114
## 174 Im11 ~~ Im6 4.589 -0.068 -0.068 -0.107 -0.107
## 175 Im22 ~~ C_REP1 4.583 0.041 0.041 0.134 0.134
## 176 BRAND =~ SAT_2 4.558 0.065 0.079 0.078 0.078
## 177 Im22 ~~ Im1 4.528 0.053 0.053 0.274 0.274
## 178 Im4 ~~ Im18 4.526 0.039 0.039 0.159 0.159
## 179 Im20 ~~ Im13 4.492 0.067 0.067 0.135 0.135
## 180 PRODQUAL =~ Im2 4.481 -0.130 -0.093 -0.073 -0.073
## 181 Im9 ~ FOOD 4.452 0.135 0.111 0.082 0.082
## 182 SAT =~ COM_A2 4.449 -0.118 -0.104 -0.065 -0.065
## 183 SAT_1 ~~ C_REP2 4.442 -0.022 -0.022 -0.196 -0.196
## 184 Im4 ~~ COM_A3 4.418 0.052 0.052 0.162 0.162
## 185 Im22 ~~ SAT_3 4.400 -0.078 -0.078 -0.130 -0.130
## 186 Im9 ~ PROF 4.377 0.124 0.115 0.085 0.085
## 187 PROF =~ COM_A2 4.354 -0.117 -0.108 -0.067 -0.067
## 188 Im22 ~~ Im11 4.339 0.079 0.079 0.124 0.124
## 189 Im13 ~~ Im16 4.324 -0.062 -0.062 -0.130 -0.130
## 190 Im3 ~~ Im5 4.300 -0.068 -0.068 -0.178 -0.178
## 191 SAT =~ COM_A4 4.286 0.123 0.109 0.062 0.062
## 192 SAT =~ C_CR1 4.284 -0.152 -0.134 -0.067 -0.067
## 193 BRAND =~ C_CR1 4.271 -0.106 -0.127 -0.064 -0.064
## 194 PROF =~ Im1 4.243 -0.191 -0.177 -0.133 -0.133
## 195 PROF =~ Im2 4.243 0.168 0.156 0.122 0.122
## 196 Im22 ~~ C_REP2 4.232 -0.030 -0.030 -0.189 -0.189
## 197 Im11 ~~ Im1 4.230 -0.052 -0.052 -0.211 -0.211
## 198 SAT =~ C_REP2 4.230 -0.051 -0.045 -0.072 -0.072
## 199 FRENCH =~ C_CR4 4.178 0.135 0.132 0.065 0.065
## 200 AFCOM =~ Im5 4.144 0.078 0.089 0.068 0.068
## 201 RI =~ COM_A2 4.115 -0.191 -0.113 -0.070 -0.070
## 202 Im1 ~~ C_REP3 4.114 -0.021 -0.021 -0.215 -0.215
## 203 Im14 ~~ Im6 4.087 0.028 0.028 0.152 0.152
## 204 PROF =~ C_CR1 4.082 -0.140 -0.130 -0.065 -0.065
## 205 PRODQUAL =~ Im1 4.048 0.140 0.100 0.075 0.075
## 206 RI =~ Im5 4.031 0.148 0.087 0.066 0.066
## 207 ATMOS =~ Im4 4.022 -0.052 -0.065 -0.048 -0.048
## 208 FOOD =~ C_CR4 4.017 0.155 0.128 0.064 0.064
## 209 DECO =~ COM_A2 3.972 -0.077 -0.096 -0.060 -0.060
## 210 Im12 ~~ Im7 3.960 0.046 0.046 0.242 0.242
## 211 PROF =~ SAT_1 3.932 -0.123 -0.114 -0.112 -0.112
## 212 PRODQUAL =~ C_REP3 3.918 -0.055 -0.040 -0.071 -0.071
## 213 Im4 ~~ C_CR1 3.904 -0.060 -0.060 -0.168 -0.168
## 214 PROF =~ C_REP1 3.901 0.054 0.050 0.068 0.068
## 215 Im5 ~~ Im6 3.873 -0.060 -0.060 -0.098 -0.098
## 216 Im3 ~~ Im4 3.857 0.145 0.145 0.947 0.947
## 217 FRENCH =~ COM_A3 3.843 0.108 0.105 0.065 0.065
## 218 CHOICE =~ COM_A3 3.821 0.075 0.097 0.060 0.060
## 219 Im3 ~~ Im2 3.811 0.029 0.029 0.115 0.115
## 220 SAT_2 ~~ C_REP1 3.809 0.028 0.028 0.112 0.112
## 221 Im20 ~~ Im22 3.733 0.150 0.150 0.266 0.266
## 222 CHOICE ~~ AFCOM 3.721 0.092 0.074 0.074 0.074
## 223 CHOICE ~ AFCOM 3.721 0.102 0.090 0.090 0.090
## 224 Im2 ~~ SAT_2 3.720 0.036 0.036 0.111 0.111
## 225 Im4 ~~ Im6 3.719 0.034 0.034 0.142 0.142
## 226 Im4 ~~ Im11 3.709 -0.042 -0.042 -0.137 -0.137
## 227 FOOD =~ Im5 3.638 0.106 0.087 0.066 0.066
## 228 Im20 ~~ COM_A4 3.626 0.084 0.084 0.114 0.114
## 229 SAT =~ Im13 3.580 0.091 0.080 0.067 0.067
## 230 Im11 ~~ C_REP1 3.565 0.037 0.037 0.095 0.095
## 231 COM_A1 ~~ SAT_1 3.546 -0.053 -0.053 -0.118 -0.118
## 232 Im22 ~~ SAT_1 3.543 0.050 0.050 0.138 0.138
## 233 Im12 ~~ SAT_3 3.514 0.054 0.054 0.116 0.116
## 234 AFCOM =~ Im20 3.501 -0.093 -0.107 -0.072 -0.072
## 235 Im8 ~ ATMOS 3.500 0.064 0.080 0.076 0.076
## 236 COM_A4 ~~ C_REP1 3.485 0.042 0.042 0.105 0.105
## 237 Im13 ~~ C_REP2 3.438 0.022 0.022 0.163 0.163
## 238 Im14 ~~ SAT_2 3.365 0.022 0.022 0.146 0.146
## 239 PRODQUAL =~ SAT_2 3.351 0.096 0.069 0.068 0.068
## 240 Im10 ~~ C_CR1 3.299 0.043 0.043 0.126 0.126
## 241 ATMOS =~ COM_A4 3.291 0.093 0.117 0.067 0.067
## 242 Im11 ~~ Im17 3.272 -0.049 -0.049 -0.173 -0.173
## 243 Im3 ~~ Im17 3.256 0.028 0.028 0.202 0.202
## 244 Im8 ~ PRODQUAL 3.239 0.109 0.078 0.074 0.074
## 245 Im17 ~~ C_REP1 3.216 -0.024 -0.024 -0.180 -0.180
## 246 Im1 ~~ SAT_1 3.212 0.033 0.033 0.234 0.234
## 247 Im22 ~~ COM_A1 3.209 -0.070 -0.070 -0.113 -0.113
## 248 Im14 ~~ Im7 3.169 -0.026 -0.026 -0.284 -0.284
## 249 Im20 ~~ SAT_1 3.168 -0.049 -0.049 -0.118 -0.118
## 250 Im5 ~~ Im1 3.150 0.043 0.043 0.182 0.182
## 251 Im14 ~~ C_CR1 3.145 -0.041 -0.041 -0.148 -0.148
## 252 Im11 ~~ SAT_1 3.133 0.049 0.049 0.105 0.105
## 253 PROF ~ AFCOM 3.106 0.064 0.079 0.079 0.079
## 254 PROF ~~ AFCOM 3.106 0.058 0.066 0.066 0.066
## 255 Im20 ~~ C_REP2 3.101 0.026 0.026 0.145 0.145
## 256 COI =~ C_REP2 3.084 -0.019 -0.033 -0.053 -0.053
## 257 Im13 ~~ COM_A2 3.074 -0.060 -0.060 -0.110 -0.110
## 258 Im16 ~~ SAT_1 3.070 -0.047 -0.047 -0.117 -0.117
## 259 COM_A3 ~~ C_REP3 3.054 -0.032 -0.032 -0.094 -0.094
## 260 COI =~ Im13 2.931 -0.039 -0.067 -0.055 -0.055
## 261 PROF =~ Im13 2.905 0.108 0.100 0.083 0.083
## 262 RI =~ Im10 2.903 -0.061 -0.036 -0.040 -0.040
## 263 Im16 ~~ C_REP3 2.900 -0.026 -0.026 -0.092 -0.092
## 264 FOOD =~ SAT_2 2.872 0.071 0.059 0.058 0.058
## 265 Im13 ~~ SAT_2 2.871 0.039 0.039 0.110 0.110
## 266 PROF ~ COI 2.858 0.112 0.204 0.204 0.204
## 267 AFCOM =~ C_CR4 2.852 0.106 0.121 0.060 0.060
## 268 AFCOM =~ Im16 2.849 -0.066 -0.076 -0.063 -0.063
## 269 Im5 ~~ COM_A2 2.839 0.068 0.068 0.089 0.089
## 270 Im13 ~~ C_REP1 2.836 -0.027 -0.027 -0.101 -0.101
## 271 Im2 ~~ Im17 2.835 0.030 0.030 0.170 0.170
## 272 SAT ~ ATMOS 2.834 0.064 0.091 0.091 0.091
## 273 Im18 ~~ COM_A1 2.811 -0.056 -0.056 -0.090 -0.090
## 274 Im2 ~~ Im16 2.794 0.041 0.041 0.093 0.093
## 275 Im5 ~~ C_REP1 2.784 0.031 0.031 0.084 0.084
## 276 ATMOS =~ C_CR1 2.783 -0.087 -0.109 -0.055 -0.055
## 277 Im12 ~~ Im6 2.763 -0.040 -0.040 -0.102 -0.102
## 278 Im10 ~~ Im12 2.744 0.022 0.022 0.119 0.119
## 279 PRODQUAL =~ Im4 2.735 -0.076 -0.054 -0.040 -0.040
## 280 Im18 ~~ Im6 2.731 0.044 0.044 0.087 0.087
## 281 FOOD =~ C_CR1 2.725 -0.123 -0.101 -0.051 -0.051
## 282 SAT_1 ~~ C_CR4 2.722 0.067 0.067 0.109 0.109
## 283 Im19 ~~ COM_A1 2.719 0.053 0.053 0.101 0.101
## 284 ATMOS =~ C_REP2 2.704 -0.028 -0.035 -0.057 -0.057
## 285 SAT =~ COM_A1 2.689 0.087 0.077 0.054 0.054
## 286 CHOICE =~ Im22 2.667 0.066 0.086 0.056 0.056
## 287 Im7 ~~ COM_A1 2.653 -0.050 -0.050 -0.167 -0.167
## 288 ATMOS =~ Im13 2.649 0.061 0.077 0.064 0.064
## 289 FRENCH =~ Im11 2.636 0.077 0.076 0.066 0.066
## 290 Im22 ~~ SAT_2 2.621 -0.045 -0.045 -0.109 -0.109
## 291 SAT =~ Im5 2.615 0.085 0.075 0.057 0.057
## 292 RI =~ Im16 2.613 -0.135 -0.080 -0.066 -0.066
## 293 AFCOM ~ Im15 2.578 0.062 0.054 0.064 0.054
## 294 Im3 ~~ Im11 2.576 0.036 0.036 0.090 0.090
## 295 SAT ~ Im9 2.560 0.041 0.047 0.064 0.047
## 296 COM_A1 ~~ C_REP2 2.551 0.024 0.024 0.124 0.124
## 297 CHOICE =~ Im19 2.546 -0.083 -0.108 -0.096 -0.096
## 298 CHOICE =~ Im16 2.546 0.080 0.105 0.086 0.086
## 299 COM_A1 ~~ COM_A3 2.527 -0.083 -0.083 -0.102 -0.102
## 300 Im14 ~~ Im12 2.506 -0.020 -0.020 -0.138 -0.138
## 301 FOOD =~ C_REP2 2.497 -0.036 -0.030 -0.048 -0.048
## 302 COM_A4 ~~ C_CR4 2.487 0.102 0.102 0.093 0.093
## 303 Im4 ~~ Im1 2.465 0.023 0.023 0.240 0.240
## 304 Im7 ~~ C_REP2 2.451 -0.018 -0.018 -0.238 -0.238
## 305 Im21 ~~ C_CR4 2.443 0.088 0.088 0.087 0.087
## 306 Im14 ~~ COM_A2 2.437 -0.028 -0.028 -0.119 -0.119
## 307 Im3 ~~ COM_A3 2.435 -0.039 -0.039 -0.095 -0.095
## 308 AFCOM =~ Im2 2.435 0.043 0.049 0.038 0.038
## 309 ATMOS =~ COM_A3 2.431 0.078 0.097 0.060 0.060
## 310 DECO =~ Im12 2.430 -0.055 -0.069 -0.061 -0.061
## 311 CHOICE ~ RI 2.424 0.408 0.186 0.186 0.186
## 312 Im2 ~~ C_REP2 2.419 -0.015 -0.015 -0.119 -0.119
## 313 Im10 ~~ Im11 2.406 0.027 0.027 0.090 0.090
## 314 Im2 ~~ C_CR1 2.398 0.055 0.055 0.093 0.093
## 315 Im11 ~~ C_REP2 2.388 -0.023 -0.023 -0.113 -0.113
## 316 FRENCH =~ COM_A2 2.386 -0.082 -0.080 -0.050 -0.050
## 317 FRENCH =~ Im1 2.384 -0.054 -0.053 -0.040 -0.040
## 318 Im3 ~~ Im22 2.371 0.034 0.034 0.107 0.107
## 319 AFCOM =~ Im7 2.343 -0.065 -0.074 -0.061 -0.061
## 320 CHOICE =~ C_CR4 2.322 0.074 0.096 0.048 0.048
## 321 Im14 ~~ Im20 2.315 -0.025 -0.025 -0.118 -0.118
## 322 SAT =~ Im14 2.300 0.038 0.034 0.039 0.039
## 323 RI =~ SAT_1 2.296 -0.099 -0.059 -0.058 -0.058
## 324 Im1 ~~ Im17 2.292 -0.028 -0.028 -0.324 -0.324
## 325 COI =~ Im11 2.278 0.040 0.068 0.059 0.059
## 326 Im20 ~~ Im1 2.247 -0.038 -0.038 -0.173 -0.173
## 327 SAT_2 ~~ C_CR3 2.241 0.063 0.063 0.093 0.093
## 328 Im12 ~~ Im16 2.235 0.042 0.042 0.097 0.097
## 329 COI =~ Im2 2.235 0.026 0.044 0.034 0.034
## 330 FRENCH =~ C_CR1 2.234 -0.095 -0.093 -0.047 -0.047
## 331 Im21 ~~ C_CR3 2.227 -0.085 -0.085 -0.086 -0.086
## 332 C_REP3 ~~ C_CR3 2.223 -0.035 -0.035 -0.084 -0.084
## 333 FRENCH =~ COM_A1 2.220 -0.075 -0.073 -0.051 -0.051
## 334 FOOD =~ Im20 2.215 -0.085 -0.070 -0.047 -0.047
## 335 COI =~ Im1 2.207 -0.029 -0.049 -0.037 -0.037
## 336 Im20 ~~ COM_A1 2.199 -0.059 -0.059 -0.084 -0.084
## 337 FOOD =~ Im1 2.177 -0.064 -0.053 -0.040 -0.040
## 338 Im14 ~~ COM_A3 2.174 0.027 0.027 0.111 0.111
## 339 COM_A1 ~~ C_CR3 2.150 0.086 0.086 0.085 0.085
## 340 COM_A3 ~~ SAT_1 2.146 0.045 0.045 0.094 0.094
## 341 CHOICE =~ Im21 2.143 0.057 0.074 0.054 0.054
## 342 Im2 ~~ C_REP1 2.122 0.019 0.019 0.077 0.077
## 343 SAT_1 ~~ C_CR1 2.114 -0.056 -0.056 -0.104 -0.104
## 344 Im22 ~~ Im13 2.101 -0.045 -0.045 -0.103 -0.103
## 345 Im7 ~~ COM_A2 2.095 -0.047 -0.047 -0.154 -0.154
## 346 BRAND ~ RI 2.046 -0.286 -0.141 -0.141 -0.141
## 347 COM_A2 ~~ SAT_2 2.029 -0.043 -0.043 -0.085 -0.085
## 348 Im11 ~~ Im2 2.025 0.037 0.037 0.072 0.072
## 349 Im14 ~~ C_REP3 2.024 0.010 0.010 0.103 0.103
## 350 Im18 ~~ C_REP1 2.016 0.023 0.023 0.075 0.075
## 351 PRODQUAL =~ Im16 2.011 -0.124 -0.088 -0.073 -0.073
## 352 Im22 ~~ Im19 2.000 -0.044 -0.044 -0.103 -0.103
## 353 Im5 ~~ SAT_2 1.989 0.039 0.039 0.077 0.077
## 354 Im5 ~~ Im16 1.986 -0.049 -0.049 -0.074 -0.074
## 355 AFCOM =~ SAT_1 1.973 0.040 0.045 0.044 0.044
## 356 Im4 ~~ COM_A4 1.957 -0.035 -0.035 -0.111 -0.111
## 357 PROF =~ Im7 1.948 -0.088 -0.081 -0.067 -0.067
## 358 SAT =~ Im20 1.946 -0.077 -0.068 -0.046 -0.046
## 359 COM_A2 ~~ SAT_3 1.940 0.057 0.057 0.077 0.077
## 360 Im9 ~ SAT 1.925 0.087 0.076 0.056 0.056
## 361 Im22 ~~ Im12 1.911 -0.040 -0.040 -0.102 -0.102
## 362 FOOD ~~ SAT 1.893 0.033 0.058 0.058 0.058
## 363 FOOD ~ SAT 1.893 0.071 0.075 0.075 0.075
## 364 Im13 ~~ SAT_3 1.884 -0.043 -0.043 -0.082 -0.082
## 365 CHOICE =~ Im10 1.880 -0.023 -0.029 -0.033 -0.033
## 366 CHOICE =~ Im14 1.880 0.023 0.029 0.034 0.034
## 367 PRODQUAL =~ C_REP2 1.876 0.039 0.028 0.045 0.045
## 368 BRAND =~ Im3 1.843 0.036 0.044 0.033 0.033
## 369 COI =~ Im16 1.842 -0.037 -0.062 -0.051 -0.051
## 370 PRODQUAL =~ Im17 1.831 0.123 0.088 0.070 0.070
## 371 PRODQUAL =~ Im18 1.831 -0.122 -0.087 -0.062 -0.062
## 372 FRENCH =~ SAT_3 1.821 0.061 0.060 0.053 0.053
## 373 Im12 ~~ COM_A4 1.819 -0.045 -0.045 -0.089 -0.089
## 374 ATMOS ~ Im15 1.799 0.053 0.043 0.051 0.043
## 375 SAT =~ Im17 1.793 0.061 0.053 0.043 0.043
## 376 Im22 ~~ Im2 1.763 -0.033 -0.033 -0.083 -0.083
## 377 SAT =~ Im18 1.744 -0.070 -0.062 -0.044 -0.044
## 378 Im17 ~~ COM_A1 1.735 0.036 0.036 0.133 0.133
## 379 COM_A4 ~~ SAT_3 1.731 -0.058 -0.058 -0.074 -0.074
## 380 Im12 ~~ Im13 1.694 0.095 0.095 0.277 0.277
## 381 RI =~ Im11 1.683 0.103 0.061 0.053 0.053
## 382 Im20 ~~ Im19 1.679 0.041 0.041 0.084 0.084
## 383 COM_A3 ~~ SAT_2 1.637 0.041 0.041 0.076 0.076
## 384 Im4 ~~ Im2 1.633 -0.019 -0.019 -0.095 -0.095
## 385 Im20 ~~ COM_A2 1.629 -0.053 -0.053 -0.075 -0.075
## 386 BRAND =~ C_REP1 1.607 0.025 0.030 0.040 0.040
## 387 PRODQUAL =~ Im7 1.597 0.090 0.064 0.053 0.053
## 388 PRODQUAL =~ Im6 1.597 -0.076 -0.054 -0.045 -0.045
## 389 Im10 ~~ SAT_2 1.596 -0.016 -0.016 -0.083 -0.083
## 390 COM_A2 ~~ COM_A4 1.589 -0.081 -0.081 -0.100 -0.100
## 391 Im16 ~~ C_CR4 1.582 -0.067 -0.067 -0.073 -0.073
## 392 BRAND ~ Im15 1.578 0.042 0.035 0.042 0.035
## 393 Im10 ~~ Im20 1.548 0.021 0.021 0.080 0.080
## 394 Im13 ~~ Im18 1.542 -0.033 -0.033 -0.075 -0.075
## 395 PRODQUAL =~ SAT_1 1.540 -0.064 -0.046 -0.045 -0.045
## 396 C_REP3 ~~ C_CR4 1.539 0.029 0.029 0.068 0.068
## 397 Im7 ~~ SAT_3 1.537 0.036 0.036 0.125 0.125
## 398 SAT =~ Im4 1.500 -0.041 -0.037 -0.027 -0.027
## 399 FOOD =~ Im16 1.494 -0.083 -0.069 -0.057 -0.057
## 400 Im14 ~~ Im2 1.491 0.013 0.013 0.089 0.089
## 401 Im2 ~~ SAT_1 1.463 -0.022 -0.022 -0.076 -0.076
## 402 Im1 ~~ COM_A4 1.452 -0.035 -0.035 -0.137 -0.137
## 403 FOOD =~ Im2 1.452 0.047 0.038 0.030 0.030
## 404 ATMOS =~ COM_A2 1.446 -0.058 -0.072 -0.045 -0.045
## 405 Im21 ~~ Im18 1.446 -0.039 -0.039 -0.064 -0.064
## 406 Im5 ~~ Im7 1.435 0.034 0.034 0.115 0.115
## 407 FRENCH =~ Im2 1.429 0.037 0.036 0.028 0.028
## 408 DECO =~ Im13 1.412 0.045 0.056 0.046 0.046
## 409 Im2 ~~ Im18 1.408 -0.026 -0.026 -0.063 -0.063
## 410 Im3 ~~ Im18 1.392 -0.022 -0.022 -0.070 -0.070
## 411 AFCOM ~ FOOD 1.390 0.094 0.068 0.068 0.068
## 412 PRODQUAL =~ COM_A2 1.387 -0.084 -0.060 -0.037 -0.037
## 413 Im2 ~~ C_REP3 1.386 0.013 0.013 0.061 0.061
## 414 ATMOS =~ SAT_2 1.380 0.034 0.042 0.042 0.042
## 415 Im3 ~~ C_CR1 1.380 0.036 0.036 0.079 0.079
## 416 Im7 ~~ C_REP3 1.371 0.014 0.014 0.117 0.117
## 417 Im12 ~~ COM_A3 1.362 -0.039 -0.039 -0.075 -0.075
## 418 FRENCH =~ SAT_1 1.359 0.039 0.038 0.037 0.037
## 419 Im1 ~~ C_REP2 1.349 0.011 0.011 0.185 0.185
## 420 FRENCH ~ Im15 1.325 0.035 0.036 0.043 0.036
## 421 Im7 ~~ COM_A4 1.320 0.040 0.040 0.124 0.124
## 422 PROF ~ Im8 1.314 0.034 0.037 0.039 0.037
## 423 ATMOS =~ Im17 1.312 -0.054 -0.067 -0.054 -0.054
## 424 ATMOS =~ Im18 1.312 0.053 0.067 0.048 0.048
## 425 Im16 ~~ Im7 1.310 -0.033 -0.033 -0.123 -0.123
## 426 C_REP1 ~~ C_CR3 1.300 0.033 0.033 0.065 0.065
## 427 Im4 ~~ C_CR3 1.291 0.037 0.037 0.092 0.092
## 428 Im14 ~~ Im13 1.286 0.015 0.015 0.095 0.095
## 429 COM_A1 ~~ C_CR1 1.282 -0.062 -0.062 -0.069 -0.069
## 430 ATMOS =~ C_CR3 1.272 -0.062 -0.078 -0.037 -0.037
## 431 Im12 ~~ Im17 1.270 -0.024 -0.024 -0.138 -0.138
## 432 Im12 ~~ COM_A2 1.270 0.036 0.036 0.073 0.073
## 433 COM_A4 ~~ C_REP3 1.269 -0.021 -0.021 -0.062 -0.062
## 434 Im20 ~~ SAT_2 1.258 0.032 0.032 0.068 0.068
## 435 Im21 ~~ SAT_3 1.256 0.043 0.043 0.059 0.059
## 436 SAT =~ Im1 1.251 -0.063 -0.056 -0.042 -0.042
## 437 Im12 ~~ C_REP1 1.249 -0.017 -0.017 -0.070 -0.070
## 438 COM_A1 ~~ C_REP3 1.245 0.018 0.018 0.059 0.059
## 439 Im8 ~ COI 1.231 -0.066 -0.111 -0.106 -0.106
## 440 SAT =~ Im19 1.224 -0.084 -0.074 -0.065 -0.065
## 441 Im10 ~~ C_REP3 1.223 -0.008 -0.008 -0.066 -0.066
## 442 Im19 ~~ SAT_3 1.222 -0.034 -0.034 -0.067 -0.067
## 443 Im5 ~~ Im14 1.221 0.018 0.018 0.077 0.077
## 444 Im6 ~~ Im7 1.217 0.401 0.401 1.652 1.652
## 445 FRENCH ~~ AFCOM 1.216 -0.081 -0.087 -0.087 -0.087
## 446 FRENCH ~ AFCOM 1.216 -0.090 -0.105 -0.105 -0.105
## 447 BRAND ~ Im8 1.215 -0.042 -0.035 -0.037 -0.035
## 448 Im12 ~~ SAT_1 1.214 -0.023 -0.023 -0.081 -0.081
## 449 Im6 ~~ C_REP2 1.207 0.013 0.013 0.084 0.084
## 450 AFCOM =~ Im6 1.205 0.041 0.047 0.039 0.039
## 451 Im2 ~~ COM_A3 1.197 0.032 0.032 0.060 0.060
## 452 Im1 ~~ COM_A1 1.197 0.028 0.028 0.118 0.118
## 453 Im19 ~~ SAT_2 1.188 0.026 0.026 0.074 0.074
## 454 SAT ~ Im15 1.185 0.032 0.036 0.043 0.036
## 455 Im18 ~~ C_REP3 1.181 -0.015 -0.015 -0.057 -0.057
## 456 Im12 ~~ C_CR1 1.177 -0.044 -0.044 -0.077 -0.077
## 457 Im16 ~~ C_CR1 1.171 0.055 0.055 0.068 0.068
## 458 PROF =~ Im4 1.159 -0.053 -0.050 -0.037 -0.037
## 459 AFCOM =~ Im21 1.159 0.052 0.059 0.043 0.043
## 460 COM_A1 ~~ SAT_2 1.154 0.031 0.031 0.062 0.062
## 461 PRODQUAL =~ COM_A3 1.153 0.080 0.057 0.035 0.035
## 462 BRAND =~ COM_A2 1.147 -0.044 -0.053 -0.033 -0.033
## 463 CHOICE =~ COM_A1 1.139 0.037 0.048 0.034 0.034
## 464 Im14 ~~ Im17 1.130 0.012 0.012 0.150 0.150
## 465 COM_A4 ~~ C_CR3 1.125 -0.070 -0.070 -0.065 -0.065
## 466 COM_A2 ~~ C_CR1 1.120 0.061 0.061 0.067 0.067
## 467 SAT =~ Im11 1.114 0.059 0.052 0.045 0.045
## 468 ATMOS ~~ SAT 1.112 0.041 0.048 0.048 0.048
## 469 ATMOS ~ SAT 1.112 0.089 0.062 0.062 0.062
## 470 BRAND =~ Im16 1.106 -0.056 -0.067 -0.056 -0.056
## 471 CHOICE ~ COI 1.103 0.102 0.133 0.133 0.133
## 472 SAT =~ Im2 1.102 0.053 0.046 0.036 0.036
## 473 AFCOM =~ C_CR1 1.100 -0.064 -0.073 -0.037 -0.037
## 474 FOOD =~ SAT_3 1.099 0.058 0.047 0.042 0.042
## 475 Im13 ~~ C_CR3 1.096 -0.049 -0.049 -0.068 -0.068
## 476 Im5 ~~ Im2 1.095 -0.026 -0.026 -0.053 -0.053
## 477 PROF ~ RI 1.090 0.184 0.117 0.117 0.117
## 478 Im11 ~~ COM_A3 1.075 0.046 0.046 0.054 0.054
## 479 Im6 ~~ COM_A1 1.075 0.034 0.034 0.055 0.055
## 480 AFCOM ~ DECO 1.071 0.049 0.053 0.053 0.053
## 481 Im21 ~~ Im11 1.067 -0.040 -0.040 -0.052 -0.052
## 482 Im12 ~~ SAT_2 1.067 -0.022 -0.022 -0.070 -0.070
## 483 Im3 ~~ Im12 1.063 -0.018 -0.018 -0.071 -0.071
## 484 AFCOM ~ Im8 1.061 0.045 0.039 0.041 0.039
## 485 Im22 ~~ Im18 1.054 0.033 0.033 0.064 0.064
## 486 Im12 ~~ C_CR3 1.050 0.045 0.045 0.069 0.069
## 487 Im3 ~~ COM_A2 1.048 -0.025 -0.025 -0.063 -0.063
## 488 PROF =~ Im5 1.047 0.070 0.064 0.049 0.049
## 489 AFCOM =~ Im1 1.043 -0.028 -0.033 -0.024 -0.024
## 490 SAT =~ Im22 1.039 -0.056 -0.050 -0.032 -0.032
## 491 Im11 ~~ Im7 1.031 0.030 0.030 0.098 0.098
## 492 Im5 ~~ Im19 1.017 -0.030 -0.030 -0.058 -0.058
## 493 Im1 ~~ COM_A3 1.014 -0.029 -0.029 -0.111 -0.111
## 494 Im17 ~~ COM_A4 1.004 -0.031 -0.031 -0.106 -0.106
## 495 FRENCH =~ COM_A4 1.003 0.057 0.055 0.032 0.032
## 496 Im1 ~~ Im18 0.979 0.021 0.021 0.107 0.107
## 497 Im6 ~~ SAT_1 0.966 0.022 0.022 0.061 0.061
## 498 RI =~ Im4 0.963 -0.045 -0.027 -0.020 -0.020
## 499 Im10 ~~ Im17 0.961 -0.012 -0.012 -0.113 -0.113
## 500 BRAND =~ COM_A4 0.952 -0.042 -0.051 -0.029 -0.029
## 501 ATMOS =~ Im3 0.949 0.025 0.031 0.023 0.023
## 502 COM_A1 ~~ C_REP1 0.940 -0.020 -0.020 -0.052 -0.052
## 503 Im18 ~~ SAT_1 0.938 -0.022 -0.022 -0.060 -0.060
## 504 FRENCH =~ Im5 0.935 0.044 0.043 0.032 0.032
## 505 Im20 ~~ SAT_3 0.923 0.037 0.037 0.054 0.054
## 506 Im7 ~~ C_CR4 0.917 0.042 0.042 0.102 0.102
## 507 COI =~ Im5 0.909 0.024 0.041 0.031 0.031
## 508 Im1 ~~ COM_A2 0.904 0.026 0.026 0.107 0.107
## 509 SAT =~ Im16 0.904 -0.073 -0.064 -0.053 -0.053
## 510 Im13 ~~ COM_A4 0.897 0.034 0.034 0.060 0.060
## 511 SAT =~ Im21 0.881 0.051 0.045 0.033 0.033
## 512 Im22 ~~ C_CR1 0.880 -0.049 -0.049 -0.067 -0.067
## 513 FRENCH =~ Im13 0.879 -0.040 -0.039 -0.032 -0.032
## 514 RI =~ Im7 0.874 -0.069 -0.041 -0.034 -0.034
## 515 COI =~ Im4 0.873 -0.014 -0.025 -0.018 -0.018
## 516 Im18 ~~ Im7 0.866 -0.023 -0.023 -0.094 -0.094
## 517 COI =~ COM_A1 0.866 -0.028 -0.047 -0.033 -0.033
## 518 Im20 ~~ Im18 0.861 0.030 0.030 0.052 0.052
## 519 PROF =~ COM_A1 0.858 0.049 0.046 0.032 0.032
## 520 Im14 ~~ Im21 0.856 0.015 0.015 0.068 0.068
## 521 COM_A2 ~~ C_CR3 0.843 -0.057 -0.057 -0.055 -0.055
## 522 SAT_3 ~~ C_REP3 0.841 0.015 0.015 0.048 0.048
## 523 Im20 ~~ COM_A3 0.836 -0.040 -0.040 -0.053 -0.053
## 524 DECO =~ SAT_2 0.835 0.027 0.034 0.033 0.033
## 525 Im18 ~~ COM_A2 0.834 0.032 0.032 0.051 0.051
## 526 Im4 ~~ Im22 0.833 -0.020 -0.020 -0.081 -0.081
## 527 PROF =~ Im6 0.833 0.049 0.045 0.037 0.037
## 528 BRAND =~ Im10 0.829 -0.017 -0.021 -0.023 -0.023
## 529 BRAND =~ Im14 0.829 0.017 0.020 0.024 0.024
## 530 AFCOM =~ Im14 0.828 0.016 0.019 0.022 0.022
## 531 Im19 ~~ COM_A2 0.825 -0.031 -0.031 -0.057 -0.057
## 532 Im12 ~~ Im2 0.821 -0.018 -0.018 -0.056 -0.056
## 533 Im13 ~~ Im6 0.818 0.023 0.023 0.053 0.053
## 534 PROF =~ Im22 0.815 0.058 0.054 0.035 0.035
## 535 Im19 ~~ SAT_1 0.808 -0.021 -0.021 -0.068 -0.068
## 536 Im4 ~~ Im7 0.801 -0.015 -0.015 -0.129 -0.129
## 537 SAT_3 ~~ C_CR1 0.797 0.047 0.047 0.054 0.054
## 538 Im11 ~~ Im18 0.795 0.029 0.029 0.045 0.045
## 539 RI =~ Im13 0.794 0.063 0.037 0.031 0.031
## 540 Im13 ~~ Im19 0.794 0.023 0.023 0.062 0.062
## 541 BRAND =~ SAT_1 0.791 -0.027 -0.032 -0.032 -0.032
## 542 Im3 ~~ SAT_1 0.785 0.014 0.014 0.062 0.062
## 543 Im12 ~~ C_CR4 0.776 0.038 0.038 0.058 0.058
## 544 Im17 ~~ Im7 0.776 -0.019 -0.019 -0.180 -0.180
## 545 Im9 ~ CHOICE 0.774 0.035 0.046 0.034 0.034
## 546 PROF =~ Im17 0.773 0.078 0.072 0.058 0.058
## 547 PROF =~ Im18 0.772 -0.078 -0.072 -0.051 -0.051
## 548 Im17 ~~ C_REP3 0.771 0.010 0.010 0.087 0.087
## 549 CHOICE =~ C_CR1 0.761 -0.041 -0.053 -0.027 -0.027
## 550 Im22 ~~ Im17 0.759 0.023 0.023 0.105 0.105
## 551 Im11 ~~ C_CR4 0.750 0.049 0.049 0.046 0.046
## 552 Im4 ~~ Im5 0.748 0.030 0.030 0.103 0.103
## 553 Im4 ~~ Im16 0.746 0.018 0.018 0.068 0.068
## 554 COM_A4 ~~ SAT_2 0.743 0.028 0.028 0.052 0.052
## 555 Im10 ~~ COM_A3 0.739 -0.017 -0.017 -0.054 -0.054
## 556 BRAND =~ Im11 0.738 -0.039 -0.047 -0.041 -0.041
## 557 Im5 ~~ Im22 0.738 0.031 0.031 0.051 0.051
## 558 BRAND =~ Im1 0.736 -0.037 -0.045 -0.034 -0.034
## 559 Im17 ~~ C_REP2 0.735 0.009 0.009 0.129 0.129
## 560 SAT =~ Im10 0.732 -0.022 -0.020 -0.022 -0.022
## 561 SAT_3 ~~ C_REP2 0.731 -0.012 -0.012 -0.066 -0.066
## 562 Im19 ~~ Im17 0.731 0.020 0.020 0.106 0.106
## 563 Im14 ~~ C_CR4 0.726 0.021 0.021 0.066 0.066
## 564 RI =~ Im6 0.725 0.054 0.032 0.027 0.027
## 565 FOOD ~ Im9 0.721 0.018 0.022 0.029 0.022
## 566 SAT ~ BRAND 0.719 0.036 0.049 0.049 0.049
## 567 AFCOM =~ SAT_3 0.719 0.033 0.037 0.033 0.033
## 568 SAT =~ C_CR3 0.712 -0.066 -0.058 -0.028 -0.028
## 569 PRODQUAL =~ Im19 0.704 0.072 0.051 0.045 0.045
## 570 ATMOS ~ Im9 0.704 0.029 0.023 0.032 0.023
## 571 Im22 ~~ Im6 0.701 0.026 0.026 0.052 0.052
## 572 ATMOS =~ Im2 0.700 -0.028 -0.035 -0.028 -0.028
## 573 Im10 ~~ C_CR4 0.698 -0.021 -0.021 -0.053 -0.053
## 574 Im21 ~~ C_REP1 0.692 -0.016 -0.016 -0.044 -0.044
## 575 Im22 ~~ COM_A3 0.689 0.035 0.035 0.053 0.053
## 576 SAT_1 ~~ C_CR3 0.683 -0.034 -0.034 -0.056 -0.056
## 577 Im13 ~~ Im7 0.677 -0.020 -0.020 -0.096 -0.096
## 578 Im5 ~~ C_REP2 0.677 -0.011 -0.011 -0.060 -0.060
## 579 Im11 ~~ COM_A1 0.673 -0.033 -0.033 -0.042 -0.042
## 580 Im11 ~~ COM_A2 0.671 0.034 0.034 0.043 0.043
## 581 Im5 ~~ Im11 0.670 0.031 0.031 0.039 0.039
## 582 Im10 ~~ C_CR3 0.668 -0.021 -0.021 -0.054 -0.054
## 583 PROF =~ Im11 0.667 0.052 0.048 0.042 0.042
## 584 Im22 ~~ COM_A4 0.663 0.035 0.035 0.054 0.054
## 585 COM_A3 ~~ SAT_3 0.663 -0.035 -0.035 -0.044 -0.044
## 586 COI =~ SAT_3 0.661 -0.021 -0.036 -0.032 -0.032
## 587 Im10 ~~ COM_A4 0.653 -0.016 -0.016 -0.052 -0.052
## 588 Im20 ~~ Im7 0.651 0.024 0.024 0.087 0.087
## 589 Im7 ~~ COM_A3 0.649 0.027 0.027 0.084 0.084
## 590 COI =~ C_REP3 0.642 -0.009 -0.015 -0.027 -0.027
## 591 Im17 ~~ COM_A3 0.642 0.024 0.024 0.082 0.082
## 592 Im22 ~~ Im7 0.641 0.024 0.024 0.098 0.098
## 593 COI =~ COM_A3 0.638 -0.026 -0.044 -0.027 -0.027
## 594 Im10 ~~ COM_A1 0.636 -0.014 -0.014 -0.049 -0.049
## 595 SAT ~ PRODQUAL 0.635 0.057 0.046 0.046 0.046
## 596 Im6 ~~ C_CR4 0.631 -0.037 -0.037 -0.044 -0.044
## 597 C_REP2 ~~ C_CR3 0.629 0.017 0.017 0.066 0.066
## 598 Im16 ~~ COM_A3 0.629 0.033 0.033 0.045 0.045
## 599 Im4 ~~ Im12 0.620 0.013 0.013 0.069 0.069
## 600 Im14 ~~ Im18 0.616 -0.011 -0.011 -0.058 -0.058
## 601 BRAND =~ SAT_3 0.604 -0.030 -0.037 -0.033 -0.033
## 602 Im5 ~~ C_CR4 0.597 0.042 0.042 0.041 0.041
## 603 PRODQUAL =~ Im22 0.595 -0.060 -0.043 -0.028 -0.028
## 604 Im14 ~~ C_CR3 0.587 0.019 0.019 0.061 0.061
## 605 ATMOS =~ Im16 0.586 -0.035 -0.044 -0.036 -0.036
## 606 Im21 ~~ COM_A4 0.583 -0.034 -0.034 -0.043 -0.043
## 607 Im4 ~~ C_REP3 0.580 -0.007 -0.007 -0.056 -0.056
## 608 Im16 ~~ COM_A4 0.580 -0.032 -0.032 -0.044 -0.044
## 609 Im19 ~~ Im18 0.577 -0.020 -0.020 -0.047 -0.047
## 610 BRAND =~ Im2 0.565 0.029 0.035 0.027 0.027
## 611 Im17 ~~ SAT_2 0.565 0.015 0.015 0.081 0.081
## 612 AFCOM ~ BRAND 0.546 0.040 0.042 0.042 0.042
## 613 RI =~ Im18 0.539 -0.051 -0.030 -0.022 -0.022
## 614 COM_A4 ~~ C_REP2 0.534 -0.012 -0.012 -0.060 -0.060
## 615 Im20 ~~ Im2 0.522 -0.018 -0.018 -0.041 -0.041
## 616 FRENCH =~ SAT_2 0.520 0.025 0.024 0.024 0.024
## 617 Im19 ~~ COM_A3 0.500 -0.025 -0.025 -0.044 -0.044
## 618 Im21 ~~ SAT_2 0.500 -0.020 -0.020 -0.041 -0.041
## 619 Im16 ~~ SAT_3 0.497 0.026 0.026 0.039 0.039
## 620 BRAND ~ COI 0.495 -0.056 -0.079 -0.079 -0.079
## 621 Im10 ~~ SAT_3 0.495 0.012 0.012 0.043 0.043
## 622 Im6 ~~ COM_A3 0.489 -0.025 -0.025 -0.038 -0.038
## 623 CHOICE =~ Im3 0.486 -0.016 -0.021 -0.016 -0.016
## 624 C_REP3 ~~ C_CR1 0.486 0.015 0.015 0.041 0.041
## 625 Im13 ~~ COM_A3 0.484 -0.025 -0.025 -0.043 -0.043
## 626 CHOICE =~ Im11 0.479 -0.027 -0.035 -0.030 -0.030
## 627 DECO ~ RI 0.474 -0.168 -0.080 -0.080 -0.080
## 628 PRODQUAL =~ COM_A1 0.474 0.046 0.033 0.023 0.023
## 629 Im3 ~~ Im19 0.473 0.013 0.013 0.047 0.047
## 630 Im17 ~~ Im6 0.472 0.015 0.015 0.068 0.068
## 631 FRENCH ~ RI 0.467 0.167 0.101 0.101 0.101
## 632 Im10 ~~ Im18 0.463 0.010 0.010 0.041 0.041
## 633 COI =~ Im19 0.461 0.019 0.031 0.028 0.028
## 634 Im1 ~~ C_CR1 0.459 -0.024 -0.024 -0.084 -0.084
## 635 Im13 ~~ COM_A1 0.456 0.022 0.022 0.041 0.041
## 636 Im6 ~~ SAT_3 0.452 -0.021 -0.021 -0.035 -0.035
## 637 SAT_1 ~~ C_REP1 0.452 0.009 0.009 0.042 0.042
## 638 FOOD =~ Im22 0.446 0.039 0.032 0.021 0.021
## 639 Im20 ~~ C_REP3 0.443 -0.011 -0.011 -0.037 -0.037
## 640 Im21 ~~ Im17 0.443 0.018 0.018 0.067 0.067
## 641 Im3 ~~ Im20 0.441 -0.015 -0.015 -0.042 -0.042
## 642 COM_A2 ~~ C_REP2 0.440 -0.010 -0.010 -0.054 -0.054
## 643 ATMOS =~ Im10 0.426 -0.012 -0.015 -0.017 -0.017
## 644 ATMOS =~ Im14 0.425 0.012 0.015 0.017 0.017
## 645 Im11 ~~ SAT_2 0.424 -0.019 -0.019 -0.036 -0.036
## 646 FOOD =~ Im4 0.422 -0.023 -0.019 -0.014 -0.014
## 647 DECO ~ Im15 0.422 0.023 0.018 0.022 0.018
## 648 COM_A1 ~~ C_CR4 0.422 -0.038 -0.038 -0.036 -0.036
## 649 AFCOM =~ Im10 0.418 -0.012 -0.014 -0.015 -0.015
## 650 RI =~ Im20 0.417 0.055 0.032 0.022 0.022
## 651 Im19 ~~ C_REP3 0.417 0.008 0.008 0.039 0.039
## 652 COI =~ Im22 0.416 -0.018 -0.031 -0.020 -0.020
## 653 Im10 ~~ Im2 0.412 -0.007 -0.007 -0.039 -0.039
## 654 Im22 ~~ COM_A2 0.409 0.026 0.026 0.042 0.042
## 655 COM_A2 ~~ C_CR4 0.406 -0.039 -0.039 -0.037 -0.037
## 656 FOOD ~ Im15 0.406 -0.015 -0.018 -0.022 -0.018
## 657 PRODQUAL =~ Im20 0.404 0.048 0.034 0.023 0.023
## 658 Im12 ~~ C_REP2 0.404 0.007 0.007 0.058 0.058
## 659 Im17 ~~ SAT_3 0.403 -0.017 -0.017 -0.063 -0.063
## 660 RI =~ Im2 0.400 0.034 0.020 0.016 0.016
## 661 FOOD =~ COM_A2 0.396 -0.037 -0.030 -0.019 -0.019
## 662 FOOD =~ COM_A1 0.394 -0.035 -0.029 -0.020 -0.020
## 663 Im21 ~~ COM_A1 0.389 0.025 0.025 0.033 0.033
## 664 ATMOS =~ Im1 0.389 0.024 0.030 0.022 0.022
## 665 FOOD =~ Im19 0.388 -0.042 -0.035 -0.031 -0.031
## 666 Im17 ~~ C_CR1 0.386 -0.023 -0.023 -0.072 -0.072
## 667 DECO =~ Im11 0.386 0.025 0.031 0.027 0.027
## 668 ATMOS ~ Im8 0.383 0.028 0.022 0.023 0.022
## 669 Im5 ~~ Im21 0.382 -0.023 -0.023 -0.031 -0.031
## 670 Im10 ~~ Im22 0.380 -0.010 -0.010 -0.044 -0.044
## 671 Im6 ~~ COM_A2 0.378 0.021 0.021 0.034 0.034
## 672 SAT =~ Im6 0.376 0.027 0.024 0.020 0.020
## 673 CHOICE ~ Im8 0.374 -0.026 -0.020 -0.021 -0.020
## 674 COI =~ Im3 0.367 0.009 0.016 0.012 0.012
## 675 COI =~ Im21 0.362 0.017 0.028 0.020 0.020
## 676 CHOICE =~ SAT_2 0.362 -0.019 -0.025 -0.025 -0.025
## 677 Im2 ~~ COM_A1 0.362 -0.016 -0.016 -0.032 -0.032
## 678 COM_A2 ~~ SAT_1 0.358 -0.018 -0.018 -0.039 -0.039
## 679 Im2 ~~ COM_A4 0.352 0.017 0.017 0.033 0.033
## 680 Im5 ~~ C_CR3 0.349 -0.033 -0.033 -0.032 -0.032
## 681 Im5 ~~ COM_A4 0.345 -0.025 -0.025 -0.031 -0.031
## 682 Im14 ~~ C_REP1 0.333 0.005 0.005 0.042 0.042
## 683 Im10 ~~ Im19 0.332 -0.008 -0.008 -0.041 -0.041
## 684 Im3 ~~ Im7 0.330 -0.010 -0.010 -0.065 -0.065
## 685 Im14 ~~ SAT_1 0.321 -0.007 -0.007 -0.049 -0.049
## 686 Im16 ~~ COM_A1 0.318 -0.021 -0.021 -0.031 -0.031
## 687 DECO =~ SAT_3 0.318 -0.021 -0.026 -0.023 -0.023
## 688 Im2 ~~ Im7 0.317 0.011 0.011 0.057 0.057
## 689 Im19 ~~ Im7 0.310 0.014 0.014 0.069 0.069
## 690 Im7 ~~ C_CR1 0.309 -0.023 -0.023 -0.065 -0.065
## 691 Im3 ~~ SAT_2 0.308 -0.009 -0.009 -0.036 -0.036
## 692 Im22 ~~ Im16 0.307 0.020 0.020 0.036 0.036
## 693 BRAND =~ C_REP2 0.306 0.009 0.011 0.017 0.017
## 694 Im2 ~~ Im19 0.306 -0.012 -0.012 -0.034 -0.034
## 695 CHOICE =~ C_CR3 0.300 -0.027 -0.035 -0.017 -0.017
## 696 Im5 ~~ COM_A1 0.296 -0.021 -0.021 -0.028 -0.028
## 697 PRODQUAL =~ Im10 0.294 -0.021 -0.015 -0.017 -0.017
## 698 PRODQUAL =~ Im14 0.294 0.021 0.015 0.017 0.017
## 699 Im21 ~~ Im16 0.292 -0.020 -0.020 -0.030 -0.030
## 700 DECO =~ Im1 0.291 -0.019 -0.024 -0.018 -0.018
## 701 DECO =~ Im2 0.291 0.017 0.021 0.016 0.016
## 702 AFCOM =~ Im4 0.290 -0.013 -0.014 -0.011 -0.011
## 703 AFCOM =~ Im13 0.286 -0.019 -0.021 -0.018 -0.018
## 704 Im7 ~~ SAT_2 0.286 -0.012 -0.012 -0.058 -0.058
## 705 AFCOM =~ C_CR3 0.285 -0.034 -0.039 -0.019 -0.019
## 706 RI =~ Im1 0.283 -0.032 -0.019 -0.014 -0.014
## 707 CHOICE =~ Im4 0.281 -0.012 -0.016 -0.012 -0.012
## 708 Im14 ~~ C_REP2 0.280 -0.003 -0.003 -0.057 -0.057
## 709 Im5 ~~ Im17 0.279 0.014 0.014 0.050 0.050
## 710 COM_A3 ~~ C_CR3 0.278 0.034 0.034 0.031 0.031
## 711 Im20 ~~ C_CR1 0.277 0.028 0.028 0.034 0.034
## 712 RI =~ C_CR1 0.276 -0.056 -0.033 -0.017 -0.017
## 713 SAT_2 ~~ C_CR1 0.275 -0.021 -0.021 -0.034 -0.034
## 714 FOOD ~~ AFCOM 0.273 0.016 0.020 0.020 0.020
## 715 FOOD ~ AFCOM 0.273 0.017 0.024 0.024 0.024
## 716 Im1 ~~ SAT_3 0.272 0.013 0.013 0.056 0.056
## 717 Im6 ~~ C_REP3 0.269 -0.007 -0.007 -0.027 -0.027
## 718 PROF =~ Im3 0.266 0.025 0.023 0.017 0.017
## 719 SAT_2 ~~ C_CR4 0.258 0.021 0.021 0.031 0.031
## 720 Im16 ~~ C_CR3 0.258 -0.028 -0.028 -0.030 -0.030
## 721 Im14 ~~ Im11 0.257 0.008 0.008 0.035 0.035
## 722 COM_A2 ~~ C_REP3 0.256 -0.009 -0.009 -0.028 -0.028
## 723 Im17 ~~ COM_A2 0.252 -0.014 -0.014 -0.052 -0.052
## 724 Im11 ~~ COM_A4 0.250 0.022 0.022 0.027 0.027
## 725 CHOICE =~ COM_A4 0.248 -0.019 -0.025 -0.014 -0.014
## 726 Im10 ~~ SAT_1 0.245 0.006 0.006 0.035 0.035
## 727 DECO =~ SAT_1 0.245 -0.015 -0.019 -0.018 -0.018
## 728 Im10 ~~ Im21 0.243 -0.008 -0.008 -0.030 -0.030
## 729 Im21 ~~ Im2 0.242 0.013 0.013 0.026 0.026
## 730 Im21 ~~ COM_A2 0.242 0.020 0.020 0.027 0.027
## 731 CHOICE =~ Im17 0.237 0.020 0.026 0.021 0.021
## 732 CHOICE =~ Im18 0.237 -0.020 -0.026 -0.019 -0.019
## 733 Im8 ~ CHOICE 0.237 -0.015 -0.020 -0.019 -0.019
## 734 RI =~ COM_A4 0.233 0.049 0.029 0.016 0.016
## 735 Im20 ~~ C_REP1 0.233 -0.009 -0.009 -0.027 -0.027
## 736 Im16 ~~ C_REP1 0.232 0.009 0.009 0.027 0.027
## 737 RI =~ COM_A3 0.231 0.047 0.028 0.017 0.017
## 738 Im21 ~~ Im1 0.231 0.012 0.012 0.052 0.052
## 739 FOOD =~ Im21 0.228 0.027 0.022 0.016 0.016
## 740 Im6 ~~ C_CR1 0.227 0.021 0.021 0.028 0.028
## 741 FRENCH =~ Im3 0.227 -0.014 -0.013 -0.010 -0.010
## 742 DECO =~ C_REP2 0.219 -0.007 -0.009 -0.014 -0.014
## 743 PRODQUAL =~ Im3 0.218 0.021 0.015 0.011 0.011
## 744 RI =~ Im19 0.217 0.039 0.023 0.020 0.020
## 745 ATMOS ~ RI 0.217 -0.153 -0.072 -0.072 -0.072
## 746 Im1 ~~ Im6 0.216 -0.010 -0.010 -0.050 -0.050
## 747 Im12 ~~ C_REP3 0.215 -0.006 -0.006 -0.028 -0.028
## 748 Im4 ~~ SAT_1 0.215 -0.007 -0.007 -0.041 -0.041
## 749 Im17 ~~ SAT_1 0.211 0.009 0.009 0.054 0.054
## 750 Im21 ~~ C_CR1 0.207 0.024 0.024 0.028 0.028
## 751 COI =~ SAT_1 0.203 -0.009 -0.016 -0.015 -0.015
## 752 BRAND =~ Im19 0.202 0.024 0.028 0.025 0.025
## 753 AFCOM ~ Im9 0.201 0.015 0.013 0.018 0.013
## 754 Im4 ~~ SAT_2 0.200 -0.007 -0.007 -0.036 -0.036
## 755 PRODQUAL =~ COM_A4 0.197 -0.034 -0.024 -0.014 -0.014
## 756 Im1 ~~ Im16 0.196 -0.011 -0.011 -0.051 -0.051
## 757 Im16 ~~ SAT_2 0.196 0.012 0.012 0.027 0.027
## 758 Im3 ~~ COM_A1 0.195 -0.010 -0.010 -0.026 -0.026
## 759 Im15 ~ FRENCH 0.191 0.022 0.021 0.018 0.018
## 760 Im14 ~~ Im1 0.186 -0.005 -0.005 -0.065 -0.065
## 761 Im2 ~~ C_CR4 0.185 -0.016 -0.016 -0.024 -0.024
## 762 Im14 ~~ Im22 0.183 0.007 0.007 0.037 0.037
## 763 CHOICE =~ SAT_1 0.182 0.014 0.018 0.018 0.018
## 764 FOOD =~ C_REP3 0.182 -0.010 -0.008 -0.014 -0.014
## 765 Im18 ~~ C_REP2 0.179 -0.005 -0.005 -0.033 -0.033
## 766 Im13 ~~ SAT_1 0.177 -0.009 -0.009 -0.030 -0.030
## 767 Im21 ~~ Im7 0.175 -0.012 -0.012 -0.042 -0.042
## 768 Im18 ~~ C_CR1 0.175 0.019 0.019 0.025 0.025
## 769 Im19 ~~ COM_A4 0.173 -0.015 -0.015 -0.027 -0.027
## 770 Im5 ~~ SAT_3 0.172 -0.015 -0.015 -0.021 -0.021
## 771 Im16 ~~ Im18 0.170 -0.013 -0.013 -0.023 -0.023
## 772 Im17 ~~ C_CR4 0.170 0.016 0.016 0.044 0.044
## 773 CHOICE =~ Im6 0.169 -0.012 -0.015 -0.013 -0.013
## 774 Im11 ~~ C_CR1 0.169 -0.022 -0.022 -0.024 -0.024
## 775 DECO =~ C_CR3 0.167 0.021 0.026 0.013 0.013
## 776 CHOICE =~ C_REP2 0.166 -0.006 -0.008 -0.012 -0.012
## 777 Im12 ~~ COM_A1 0.162 0.012 0.012 0.025 0.025
## 778 COM_A3 ~~ C_CR1 0.161 -0.024 -0.024 -0.025 -0.025
## 779 FRENCH =~ C_CR3 0.160 -0.027 -0.026 -0.013 -0.013
## 780 SAT_3 ~~ C_CR4 0.159 0.022 0.022 0.022 0.022
## 781 Im4 ~~ COM_A2 0.155 -0.009 -0.009 -0.031 -0.031
## 782 Im3 ~~ C_REP3 0.155 0.004 0.004 0.023 0.023
## 783 Im5 ~~ SAT_1 0.153 -0.010 -0.010 -0.023 -0.023
## 784 FRENCH =~ Im18 0.151 0.016 0.016 0.011 0.011
## 785 FRENCH =~ Im17 0.151 -0.016 -0.016 -0.013 -0.013
## 786 SAT =~ C_REP3 0.149 -0.009 -0.008 -0.015 -0.015
## 787 Im4 ~~ COM_A1 0.149 0.009 0.009 0.029 0.029
## 788 Im11 ~~ Im16 0.148 -0.014 -0.014 -0.020 -0.020
## 789 Im19 ~~ C_CR3 0.145 0.018 0.018 0.025 0.025
## 790 Im7 ~~ C_REP1 0.143 0.006 0.006 0.038 0.038
## 791 AFCOM =~ Im18 0.141 -0.013 -0.015 -0.011 -0.011
## 792 FOOD =~ COM_A4 0.140 -0.023 -0.019 -0.011 -0.011
## 793 Im4 ~~ C_REP2 0.140 0.003 0.003 0.041 0.041
## 794 Im22 ~~ C_CR3 0.139 0.021 0.021 0.025 0.025
## 795 Im3 ~~ C_CR3 0.138 -0.012 -0.012 -0.024 -0.024
## 796 Im14 ~~ COM_A1 0.138 0.006 0.006 0.027 0.027
## 797 Im3 ~~ C_REP2 0.137 -0.003 -0.003 -0.032 -0.032
## 798 C_CR1 ~~ C_CR3 0.136 0.097 0.097 0.080 0.080
## 799 CHOICE =~ COM_A2 0.135 -0.013 -0.017 -0.011 -0.011
## 800 DECO ~ Im8 0.131 0.014 0.012 0.012 0.012
## 801 DECO ~ Im9 0.128 0.011 0.009 0.012 0.009
## 802 Im1 ~~ Im2 0.127 0.290 0.290 1.859 1.859
## 803 CHOICE ~ SAT 0.127 -0.089 -0.060 -0.060 -0.060
## 804 CHOICE ~~ SAT 0.127 -0.041 -0.047 -0.047 -0.047
## 805 Im21 ~~ Im12 0.125 0.010 0.010 0.022 0.022
## 806 Im20 ~~ Im11 0.124 0.014 0.014 0.019 0.019
## 807 PROF =~ C_CR3 0.123 -0.026 -0.024 -0.011 -0.011
## 808 Im3 ~~ SAT_3 0.122 -0.008 -0.008 -0.020 -0.020
## 809 Im20 ~~ Im12 0.121 0.010 0.010 0.023 0.023
## 810 Im17 ~~ C_CR3 0.120 0.014 0.014 0.038 0.038
## 811 C_REP2 ~~ C_CR1 0.119 0.007 0.007 0.030 0.030
## 812 FRENCH =~ Im21 0.118 -0.017 -0.016 -0.012 -0.012
## 813 COI =~ COM_A4 0.117 0.012 0.020 0.011 0.011
## 814 BRAND ~ SAT 0.116 0.024 0.018 0.018 0.018
## 815 BRAND ~~ SAT 0.116 0.011 0.014 0.014 0.014
## 816 PROF =~ Im21 0.115 0.021 0.019 0.014 0.014
## 817 Im3 ~~ C_CR4 0.115 -0.011 -0.011 -0.021 -0.021
## 818 BRAND ~ AFCOM 0.113 -0.016 -0.015 -0.015 -0.015
## 819 BRAND ~~ AFCOM 0.113 -0.014 -0.012 -0.012 -0.012
## 820 Im4 ~~ Im14 0.113 -0.003 -0.003 -0.035 -0.035
## 821 Im14 ~~ SAT_3 0.112 -0.005 -0.005 -0.024 -0.024
## 822 ATMOS =~ SAT_1 0.110 0.009 0.012 0.012 0.012
## 823 RI =~ C_CR4 0.102 0.035 0.021 0.010 0.010
## 824 DECO =~ COM_A1 0.102 -0.012 -0.015 -0.010 -0.010
## 825 Im4 ~~ C_CR4 0.100 0.010 0.010 0.025 0.025
## 826 ATMOS =~ Im19 0.100 -0.014 -0.018 -0.016 -0.016
## 827 PROF ~ Im9 0.100 -0.007 -0.008 -0.011 -0.008
## 828 AFCOM =~ Im19 0.098 -0.011 -0.012 -0.011 -0.011
## 829 Im16 ~~ C_REP2 0.095 0.004 0.004 0.025 0.025
## 830 Im1 ~~ C_CR3 0.093 -0.011 -0.011 -0.036 -0.036
## 831 DECO =~ Im16 0.092 -0.018 -0.023 -0.019 -0.019
## 832 DECO =~ Im19 0.092 0.019 0.023 0.021 0.021
## 833 CHOICE ~ Im9 0.091 -0.010 -0.008 -0.011 -0.008
## 834 Im6 ~~ SAT_2 0.090 -0.007 -0.007 -0.017 -0.017
## 835 DECO =~ COM_A4 0.088 0.012 0.015 0.009 0.009
## 836 SAT_2 ~~ C_REP3 0.083 0.003 0.003 0.016 0.016
## 837 PROF =~ SAT_3 0.083 -0.020 -0.018 -0.016 -0.016
## 838 Im18 ~~ C_CR3 0.081 -0.014 -0.014 -0.016 -0.016
## 839 FRENCH =~ C_REP3 0.081 -0.005 -0.005 -0.009 -0.009
## 840 Im2 ~~ Im6 0.081 -0.006 -0.006 -0.015 -0.015
## 841 Im20 ~~ C_CR3 0.081 -0.016 -0.016 -0.017 -0.017
## 842 Im5 ~~ Im18 0.081 0.009 0.009 0.014 0.014
## 843 ATMOS =~ SAT_3 0.079 -0.010 -0.013 -0.012 -0.012
## 844 Im18 ~~ C_CR4 0.077 -0.013 -0.013 -0.015 -0.015
## 845 Im1 ~~ C_CR4 0.073 -0.010 -0.010 -0.031 -0.031
## 846 Im18 ~~ SAT_2 0.072 0.006 0.006 0.015 0.015
## 847 Im5 ~~ Im12 0.071 0.008 0.008 0.016 0.016
## 848 Im8 ~ BRAND 0.070 -0.009 -0.011 -0.010 -0.010
## 849 COI =~ Im12 0.069 0.006 0.010 0.009 0.009
## 850 Im11 ~~ Im19 0.068 -0.008 -0.008 -0.015 -0.015
## 851 SAT_1 ~~ C_REP3 0.067 0.003 0.003 0.016 0.016
## 852 Im2 ~~ COM_A2 0.067 -0.007 -0.007 -0.014 -0.014
## 853 Im6 ~~ C_REP1 0.063 -0.004 -0.004 -0.013 -0.013
## 854 COI =~ Im20 0.062 0.007 0.012 0.008 0.008
## 855 Im12 ~~ Im18 0.062 -0.006 -0.006 -0.016 -0.016
## 856 Im18 ~~ COM_A4 0.061 -0.009 -0.009 -0.014 -0.014
## 857 FOOD =~ Im17 0.061 0.013 0.010 0.008 0.008
## 858 FOOD =~ Im18 0.061 -0.012 -0.010 -0.007 -0.007
## 859 DECO ~~ AFCOM 0.061 -0.011 -0.009 -0.009 -0.009
## 860 DECO ~ AFCOM 0.061 -0.012 -0.011 -0.011 -0.011
## 861 FRENCH =~ Im10 0.060 -0.010 -0.010 -0.011 -0.011
## 862 FRENCH =~ Im14 0.060 0.010 0.010 0.011 0.011
## 863 Im10 ~~ C_REP2 0.059 -0.002 -0.002 -0.021 -0.021
## 864 Im4 ~~ Im20 0.058 -0.005 -0.005 -0.019 -0.019
## 865 RI =~ C_CR3 0.056 0.027 0.016 0.008 0.008
## 866 Im2 ~~ C_CR3 0.056 0.009 0.009 0.014 0.014
## 867 COI =~ Im17 0.055 -0.005 -0.009 -0.007 -0.007
## 868 Im4 ~~ Im21 0.055 0.005 0.005 0.018 0.018
## 869 FOOD ~ COI 0.052 -0.013 -0.027 -0.027 -0.027
## 870 Im21 ~~ Im13 0.051 -0.007 -0.007 -0.014 -0.014
## 871 COI =~ Im6 0.051 -0.005 -0.008 -0.007 -0.007
## 872 RI =~ Im17 0.050 0.015 0.009 0.007 0.007
## 873 Im21 ~~ COM_A3 0.050 -0.010 -0.010 -0.012 -0.012
## 874 COM_A2 ~~ C_REP1 0.049 0.005 0.005 0.012 0.012
## 875 CHOICE =~ SAT_3 0.049 0.009 0.011 0.010 0.010
## 876 BRAND =~ C_CR3 0.048 -0.012 -0.014 -0.007 -0.007
## 877 Im19 ~~ Im6 0.044 -0.005 -0.005 -0.013 -0.013
## 878 Im4 ~~ SAT_3 0.043 0.004 0.004 0.015 0.015
## 879 C_REP1 ~~ C_CR1 0.043 -0.006 -0.006 -0.012 -0.012
## 880 AFCOM =~ Im3 0.042 -0.005 -0.006 -0.004 -0.004
## 881 Im3 ~~ Im13 0.042 0.004 0.004 0.014 0.014
## 882 PRODQUAL =~ Im21 0.042 0.015 0.011 0.008 0.008
## 883 Im1 ~~ Im19 0.041 -0.004 -0.004 -0.027 -0.027
## 884 FOOD =~ C_CR3 0.041 -0.016 -0.013 -0.006 -0.006
## 885 C_CR1 ~~ C_CR4 0.039 -0.046 -0.046 -0.038 -0.038
## 886 SAT_3 ~~ C_REP1 0.037 -0.004 -0.004 -0.010 -0.010
## 887 Im11 ~~ C_CR3 0.036 0.011 0.011 0.010 0.010
## 888 Im11 ~~ SAT_3 0.035 -0.007 -0.007 -0.009 -0.009
## 889 DECO =~ Im10 0.035 -0.004 -0.005 -0.005 -0.005
## 890 DECO =~ Im14 0.035 0.004 0.005 0.005 0.005
## 891 Im10 ~~ Im1 0.034 -0.002 -0.002 -0.023 -0.023
## 892 PRODQUAL =~ SAT_3 0.032 0.012 0.009 0.008 0.008
## 893 PRODQUAL ~ SAT 0.031 -0.008 -0.010 -0.010 -0.010
## 894 PRODQUAL ~~ SAT 0.031 -0.004 -0.008 -0.008 -0.008
## 895 RI =~ SAT_3 0.031 -0.014 -0.008 -0.008 -0.008
## 896 SAT =~ Im7 0.029 -0.008 -0.007 -0.006 -0.006
## 897 Im3 ~~ Im16 0.029 -0.004 -0.004 -0.011 -0.011
## 898 FRENCH =~ Im19 0.028 0.009 0.008 0.007 0.007
## 899 DECO =~ Im21 0.028 -0.007 -0.008 -0.006 -0.006
## 900 COI =~ Im14 0.027 -0.002 -0.003 -0.004 -0.004
## 901 FRENCH =~ Im4 0.027 0.005 0.005 0.003 0.003
## 902 PRODQUAL ~ Im8 0.027 0.004 0.006 0.006 0.006
## 903 FOOD =~ SAT_1 0.027 -0.007 -0.006 -0.005 -0.005
## 904 FOOD =~ Im3 0.026 -0.006 -0.005 -0.004 -0.004
## 905 Im3 ~~ Im21 0.026 -0.004 -0.004 -0.009 -0.009
## 906 PROF =~ C_REP2 0.026 0.004 0.003 0.005 0.005
## 907 Im1 ~~ Im7 0.025 -0.003 -0.003 -0.034 -0.034
## 908 Im13 ~~ C_CR1 0.024 -0.007 -0.007 -0.010 -0.010
## 909 C_CR3 ~~ C_CR4 0.023 -0.036 -0.036 -0.026 -0.026
## 910 Im2 ~~ SAT_3 0.023 -0.004 -0.004 -0.008 -0.008
## 911 Im3 ~~ Im10 0.022 0.001 0.001 0.010 0.010
## 912 Im5 ~~ Im10 0.022 -0.002 -0.002 -0.009 -0.009
## 913 Im13 ~~ C_CR4 0.022 0.007 0.007 0.009 0.009
## 914 Im5 ~~ C_REP3 0.021 0.002 0.002 0.007 0.007
## 915 PRODQUAL =~ C_REP1 0.020 0.005 0.003 0.005 0.005
## 916 Im3 ~~ Im14 0.019 -0.001 -0.001 -0.011 -0.011
## 917 Im3 ~~ C_REP1 0.019 0.002 0.002 0.008 0.008
## 918 SAT =~ Im3 0.019 0.005 0.004 0.003 0.003
## 919 Im22 ~~ C_CR4 0.019 0.008 0.008 0.009 0.009
## 920 BRAND =~ Im21 0.019 -0.006 -0.007 -0.005 -0.005
## 921 Im20 ~~ C_CR4 0.018 -0.008 -0.008 -0.008 -0.008
## 922 Im5 ~~ C_CR1 0.018 0.007 0.007 0.008 0.008
## 923 Im4 ~~ C_REP1 0.018 -0.001 -0.001 -0.010 -0.010
## 924 Im14 ~~ COM_A4 0.018 0.003 0.003 0.010 0.010
## 925 Im18 ~~ COM_A3 0.018 0.005 0.005 0.007 0.007
## 926 COI =~ Im7 0.018 -0.003 -0.006 -0.005 -0.005
## 927 C_REP1 ~~ C_CR4 0.018 -0.004 -0.004 -0.007 -0.007
## 928 Im3 ~~ Im6 0.017 0.002 0.002 0.008 0.008
## 929 Im20 ~~ Im16 0.015 0.005 0.005 0.007 0.007
## 930 Im4 ~~ Im19 0.015 -0.002 -0.002 -0.011 -0.011
## 931 COI =~ Im10 0.014 0.001 0.002 0.003 0.003
## 932 Im6 ~~ COM_A4 0.014 -0.004 -0.004 -0.007 -0.007
## 933 Im10 ~~ C_REP1 0.013 0.001 0.001 0.007 0.007
## 934 Im7 ~~ SAT_1 0.011 0.002 0.002 0.013 0.013
## 935 SAT_2 ~~ C_REP2 0.010 0.001 0.001 0.008 0.008
## 936 Im1 ~~ C_REP1 0.010 -0.001 -0.001 -0.011 -0.011
## 937 AFCOM =~ Im17 0.010 0.003 0.003 0.003 0.003
## 938 Im12 ~~ Im1 0.009 0.002 0.002 0.012 0.012
## 939 COM_A3 ~~ C_CR4 0.008 0.006 0.006 0.005 0.005
## 940 Im7 ~~ C_CR3 0.008 -0.004 -0.004 -0.010 -0.010
## 941 PRODQUAL =~ C_CR3 0.007 -0.008 -0.006 -0.003 -0.003
## 942 Im13 ~~ C_REP3 0.006 0.001 0.001 0.005 0.005
## 943 COM_A4 ~~ C_CR1 0.006 0.005 0.005 0.005 0.005
## 944 Im16 ~~ Im6 0.006 -0.002 -0.002 -0.004 -0.004
## 945 Im5 ~~ Im13 0.006 -0.002 -0.002 -0.004 -0.004
## 946 Im21 ~~ Im6 0.005 -0.002 -0.002 -0.004 -0.004
## 947 DECO ~ COI 0.005 -0.006 -0.008 -0.008 -0.008
## 948 Im4 ~~ Im13 0.004 -0.001 -0.001 -0.006 -0.006
## 949 Im19 ~~ C_CR4 0.004 0.003 0.003 0.004 0.004
## 950 Im4 ~~ Im10 0.004 -0.001 -0.001 -0.005 -0.005
## 951 FRENCH =~ Im12 0.003 -0.002 -0.002 -0.002 -0.002
## 952 PROF =~ COM_A4 0.003 -0.003 -0.003 -0.002 -0.002
## 953 BRAND =~ COM_A1 0.002 0.002 0.002 0.002 0.002
## 954 Im6 ~~ C_CR3 0.002 -0.002 -0.002 -0.003 -0.003
## 955 COI =~ Im18 0.002 0.001 0.002 0.001 0.001
## 956 Im12 ~~ Im19 0.002 -0.001 -0.001 -0.003 -0.003
## 957 Im18 ~~ SAT_3 0.001 0.001 0.001 0.002 0.002
## 958 Im19 ~~ C_CR1 0.001 0.001 0.001 0.002 0.002
## 959 PROF =~ Im10 0.001 -0.001 -0.001 -0.001 -0.001
## 960 PROF =~ Im14 0.001 0.001 0.001 0.001 0.001
## 961 Im14 ~~ Im19 0.001 0.000 0.000 0.003 0.003
## 962 Im21 ~~ Im19 0.001 0.001 0.001 0.002 0.002
## 963 FOOD =~ Im12 0.001 -0.002 -0.001 -0.001 -0.001
## 964 Im16 ~~ Im17 0.001 -0.001 -0.001 -0.003 -0.003
## 965 RI =~ Im3 0.001 0.001 0.001 0.000 0.000
## 966 Im21 ~~ SAT_1 0.000 -0.001 -0.001 -0.001 -0.001
## 967 Im16 ~~ COM_A2 0.000 0.001 0.001 0.001 0.001
## 968 ATMOS =~ Im6 0.000 0.001 0.001 0.001 0.001
## 969 ATMOS =~ Im7 0.000 -0.001 -0.001 -0.001 -0.001
## 970 SAT_1 ~~ SAT_2 0.000 -0.001 -0.001 -0.003 -0.003
## 971 Im11 ~~ C_REP3 0.000 0.000 0.000 -0.001 -0.001
## 972 AFCOM =~ Im22 0.000 0.001 0.001 0.000 0.000
## 973 Im5 ~~ COM_A3 0.000 0.000 0.000 0.001 0.001
## 974 Im21 ~~ C_REP2 0.000 0.000 0.000 0.001 0.001
## 975 CHOICE =~ Im7 0.000 0.000 0.000 0.000 0.000
## 976 COI =~ COM_A2 0.000 0.000 0.000 0.000 0.000
## 977 Im5 ~~ Im20 0.000 0.000 0.000 0.000 0.000